Pub Date : 2026-01-22DOI: 10.1016/j.jmaa.2026.130453
Wenqiang Zhao , Xia Liu
This article is concerned with the random dynamics of non-autonomous stochastic reaction-diffusion equations that incorporate additive white noise and infinite delay, with the delay term being globally Lipschitz continuous. We first establish the existence of (periodic) pullback random attractors for the corresponding non-autonomous dynamical system (NRDS). The asymptotical compactness of solutions is primarily achieved by applying the Arzelà-Ascoli theorem over a compact time interval, coupled with a limiting argument for the negative infinite part. Furthermore, we demonstrate that the solution to the underlying equations is jointly continuous in both the initial time and the initial data. This result allows us to construct a family of (periodic) invariant Borel probability measures that are supported within the pullback random attractors for the NRDS.
{"title":"Invariant measure of non-autonomous stochastic reaction-diffusion equations with infinite delay and additive white noise","authors":"Wenqiang Zhao , Xia Liu","doi":"10.1016/j.jmaa.2026.130453","DOIUrl":"10.1016/j.jmaa.2026.130453","url":null,"abstract":"<div><div>This article is concerned with the random dynamics of non-autonomous stochastic reaction-diffusion equations that incorporate additive white noise and infinite delay, with the delay term being globally Lipschitz continuous. We first establish the existence of (periodic) pullback random attractors for the corresponding non-autonomous dynamical system (NRDS). The asymptotical compactness of solutions is primarily achieved by applying the Arzelà-Ascoli theorem over a compact time interval, coupled with a limiting argument for the negative infinite part. Furthermore, we demonstrate that the solution to the underlying equations is jointly continuous in both the initial time and the initial data. This result allows us to construct a family of (periodic) invariant Borel probability measures that are supported within the pullback random attractors for the NRDS.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130453"},"PeriodicalIF":1.2,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.1016/j.jmaa.2026.130446
Josiah Aakre
Many previously studied path algebras and self-similar group algebras may be viewed as Steinberg algebras of self-similar groupoids. By way of inverse semigroup algebras, we characterize when the Steinberg algebra of a self-similar groupoid is simple. We show that the simplicity of the reduced -algebra of a contracting self-similar groupoid coincides with the simplicity of the Steinberg algebra. As an aside, we show that simplicity of the two algebras sometimes depends only on the skeleton of the self-similar groupoid acting on a strongly connected graph. Finally, we apply our methods to examples including a self-similar groupoid akin to multispinal self-similar groups and a self-similar groupoid built from the well-known Basilica group.
{"title":"Simplicity of algebras and C⁎-algebras of self-similar groupoids","authors":"Josiah Aakre","doi":"10.1016/j.jmaa.2026.130446","DOIUrl":"10.1016/j.jmaa.2026.130446","url":null,"abstract":"<div><div>Many previously studied path algebras and self-similar group algebras may be viewed as Steinberg algebras of self-similar groupoids. By way of inverse semigroup algebras, we characterize when the Steinberg algebra of a self-similar groupoid is simple. We show that the simplicity of the reduced <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra of a contracting self-similar groupoid coincides with the simplicity of the Steinberg algebra. As an aside, we show that simplicity of the two algebras sometimes depends only on the skeleton of the self-similar groupoid acting on a strongly connected graph. Finally, we apply our methods to examples including a self-similar groupoid akin to multispinal self-similar groups and a self-similar groupoid built from the well-known Basilica group.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130446"},"PeriodicalIF":1.2,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.1016/j.jmaa.2026.130452
Eduardo H. Gomes Tavares , Anderson J.A. Ramos , Marcio A. Jorge Silva , JinYun Yuan
We provide a complete analytical and numerical characterization of the stability behavior for a shearing Cattaneo-Timoshenko system governed by a recently proposed stability number, denoted herein by . Unlike previous results restricted to energy-based approaches or specific parameter configurations, we prove that is not only sufficient but also necessary for exponential stability. Otherwise, the system exhibits optimal algebraic decay rate for regular initial data. The theoretical results are aligned with a proper numerical analysis where a finite difference scheme confirms the characterization of stability in terms of and its effectiveness in predicting the complete system's asymptotic behavior.
{"title":"Full stability characterization of shearing Cattaneo-Timoshenko systems","authors":"Eduardo H. Gomes Tavares , Anderson J.A. Ramos , Marcio A. Jorge Silva , JinYun Yuan","doi":"10.1016/j.jmaa.2026.130452","DOIUrl":"10.1016/j.jmaa.2026.130452","url":null,"abstract":"<div><div>We provide a complete analytical and numerical characterization of the stability behavior for a shearing Cattaneo-Timoshenko system governed by a recently proposed stability number, denoted herein by <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>τ</mi></mrow></msub></math></span>. Unlike previous results restricted to energy-based approaches or specific parameter configurations, we prove that <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>τ</mi></mrow></msub><mo>=</mo><mn>0</mn></math></span> is not only sufficient but also necessary for exponential stability. Otherwise, the system exhibits optimal algebraic decay rate <span><math><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></span> for regular initial data. The theoretical results are aligned with a proper numerical analysis where a finite difference scheme confirms the characterization of stability in terms of <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>τ</mi></mrow></msub></math></span> and its effectiveness in predicting the complete system's asymptotic behavior.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130452"},"PeriodicalIF":1.2,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-20DOI: 10.1016/j.jmaa.2026.130445
Mohammad Saeid Abolhassanifar , Reza Saadati , Mohammad Bagher Ghaemi , Donal O'Regan
<div><div>We investigate a class of nonlinear nonlocal problems that integrate two complex mechanisms: Kirchhoff-type nonlocal diffusion and Choquard-type critical convolution nonlinearity involving the Hardy–Littlewood–Sobolev (HLS) critical exponent. Specifically, we consider the following equation in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>:<span><span><span><math><mo>−</mo><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><msup><mrow><mo>(</mo><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></munder><mo>|</mo><mi>∇</mi><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mspace></mspace><mi>d</mi><mi>x</mi><mo>)</mo></mrow><mrow><mi>θ</mi></mrow></msup><mo>)</mo></mrow><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>u</mi><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>⁎</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi></mrow></msup><mo>)</mo></mrow><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo><mspace></mspace><mi>u</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo><mo>,</mo><mspace></mspace><mi>u</mi><mo>></mo><mn>0</mn><mo>,</mo></math></span></span></span> where <span><math><mi>a</mi><mo>,</mo><mi>b</mi><mo>></mo><mn>0</mn></math></span>, <span><math><mn>0</mn><mo><</mo><mi>θ</mi><mo><</mo><mfrac><mrow><mi>α</mi></mrow><mrow><mn>3</mn></mrow></mfrac></math></span>, <span><math><mn>0</mn><mo><</mo><mi>α</mi><mo><</mo><mn>3</mn></math></span>, <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow></msub></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>3</mn><mo>−</mo><mi>α</mi></mrow></msup></mrow></mfrac></math></span> is the Riesz potential, and <span><math><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is a positive, asymptotically constant potential. This formulation simultaneously captures <em>Kirchhoff-type nonlocality</em> through the energy-dependent coefficient of the Laplacian, and <em>Choquard criticality</em> via a convolution nonlinearity with critical exponent <span><math><mi>q</mi><mo>=</mo><mn>3</mn><mo>+</mo><mi>α</mi></math></span>.</div><div>By combining variational methods, Pohožaev-type identities, and global compactness techniques adapted to this doubly nonlocal setting, we prove the existence of positive ground state solutions in both subcritical and critical cases. Moreover, we analyze the asymptotic behavior as the nonlocal parameters approach their critical limits, <span><math><mi>θ</mi><mo>→</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msup></math></span> and <span><math><mi>α</
{"title":"Ground state solutions and asymptotic behavior for a nonlocal Kirchhoff–Choquard equation with variable potential in R3","authors":"Mohammad Saeid Abolhassanifar , Reza Saadati , Mohammad Bagher Ghaemi , Donal O'Regan","doi":"10.1016/j.jmaa.2026.130445","DOIUrl":"10.1016/j.jmaa.2026.130445","url":null,"abstract":"<div><div>We investigate a class of nonlinear nonlocal problems that integrate two complex mechanisms: Kirchhoff-type nonlocal diffusion and Choquard-type critical convolution nonlinearity involving the Hardy–Littlewood–Sobolev (HLS) critical exponent. Specifically, we consider the following equation in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>:<span><span><span><math><mo>−</mo><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><msup><mrow><mo>(</mo><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></munder><mo>|</mo><mi>∇</mi><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mspace></mspace><mi>d</mi><mi>x</mi><mo>)</mo></mrow><mrow><mi>θ</mi></mrow></msup><mo>)</mo></mrow><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>u</mi><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>⁎</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi></mrow></msup><mo>)</mo></mrow><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo><mspace></mspace><mi>u</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo><mo>,</mo><mspace></mspace><mi>u</mi><mo>></mo><mn>0</mn><mo>,</mo></math></span></span></span> where <span><math><mi>a</mi><mo>,</mo><mi>b</mi><mo>></mo><mn>0</mn></math></span>, <span><math><mn>0</mn><mo><</mo><mi>θ</mi><mo><</mo><mfrac><mrow><mi>α</mi></mrow><mrow><mn>3</mn></mrow></mfrac></math></span>, <span><math><mn>0</mn><mo><</mo><mi>α</mi><mo><</mo><mn>3</mn></math></span>, <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow></msub></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>3</mn><mo>−</mo><mi>α</mi></mrow></msup></mrow></mfrac></math></span> is the Riesz potential, and <span><math><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is a positive, asymptotically constant potential. This formulation simultaneously captures <em>Kirchhoff-type nonlocality</em> through the energy-dependent coefficient of the Laplacian, and <em>Choquard criticality</em> via a convolution nonlinearity with critical exponent <span><math><mi>q</mi><mo>=</mo><mn>3</mn><mo>+</mo><mi>α</mi></math></span>.</div><div>By combining variational methods, Pohožaev-type identities, and global compactness techniques adapted to this doubly nonlocal setting, we prove the existence of positive ground state solutions in both subcritical and critical cases. Moreover, we analyze the asymptotic behavior as the nonlocal parameters approach their critical limits, <span><math><mi>θ</mi><mo>→</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msup></math></span> and <span><math><mi>α</","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130445"},"PeriodicalIF":1.2,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we study the asymptotic behaviour of solutions to the heat equation in exterior domains, i.e., domains which are the complement of a smooth compact set in . Different homogeneous boundary conditions are considered, including Dirichlet, Robin, and Neumann ones. In this second part of our work, for , we consider the case of bounded initial data and prove that, after some correction term, the solutions become close to the solutions in the whole space and show how complex behaviours appear. We also analyse the case of initial data in with where all solutions essentially decay to 0 and the convergence rate could be arbitrarily slow.
{"title":"Asymptotic behaviour of the heat equation in an exterior domain with general boundary conditions II. The case of bounded and of Lp data","authors":"Joaquín Domínguez-de-Tena , Aníbal Rodríguez-Bernal","doi":"10.1016/j.jmaa.2026.130448","DOIUrl":"10.1016/j.jmaa.2026.130448","url":null,"abstract":"<div><div>In this work, we study the asymptotic behaviour of solutions to the heat equation in exterior domains, i.e., domains which are the complement of a smooth compact set in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>. Different homogeneous boundary conditions are considered, including Dirichlet, Robin, and Neumann ones. In this second part of our work, for <span><math><mi>N</mi><mo>≥</mo><mn>3</mn></math></span>, we consider the case of bounded initial data and prove that, after some correction term, the solutions become close to the solutions in the whole space and show how complex behaviours appear. We also analyse the case of initial data in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> with <span><math><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mo>∞</mo></math></span> where all solutions essentially decay to 0 and the convergence rate could be arbitrarily slow.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130448"},"PeriodicalIF":1.2,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-20DOI: 10.1016/j.jmaa.2026.130451
Yuan Chen
We investigate the mass-preserving -gradient flow associated with a generalized Cahn–Hilliard equation. Our focus is on the sharp interface regime, where the interface width parameter is small. For well-prepared initial data, we rigorously prove that, as , solutions of the diffuse-interface model converge to the volume-preserving Willmore flow in arbitrary spatial dimensions . The proof incorporates matched asymptotic expansions, spectrum and energy estimates to establish the convergence of the order parameter away from the interface, alongside a precise motion law derivation for the limiting interface. This result extends the analysis of Fei and Liu [16] from two- and three-dimensional settings to general N-dimensional domains, and it applies to a broad class of symmetric double-well potentials beyond the classical quartic form.
{"title":"Volume preserving Willmore flow in a generalized Cahn-Hilliard flow","authors":"Yuan Chen","doi":"10.1016/j.jmaa.2026.130451","DOIUrl":"10.1016/j.jmaa.2026.130451","url":null,"abstract":"<div><div>We investigate the mass-preserving <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-gradient flow associated with a generalized Cahn–Hilliard equation. Our focus is on the sharp interface regime, where the interface width parameter <span><math><mi>ε</mi><mo>></mo><mn>0</mn></math></span> is small. For well-prepared initial data, we rigorously prove that, as <span><math><mi>ε</mi><mo>→</mo><mn>0</mn></math></span>, solutions of the diffuse-interface model converge to the <em>volume-preserving Willmore flow</em> in arbitrary spatial dimensions <span><math><mi>N</mi><mo>≥</mo><mn>2</mn></math></span>. The proof incorporates matched asymptotic expansions, spectrum and energy estimates to establish the convergence of the order parameter away from the interface, alongside a precise motion law derivation for the limiting interface. This result extends the analysis of Fei and Liu <span><span>[16]</span></span> from two- and three-dimensional settings to general <em>N</em>-dimensional domains, and it applies to a broad class of symmetric double-well potentials beyond the classical quartic form.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130451"},"PeriodicalIF":1.2,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-20DOI: 10.1016/j.jmaa.2026.130450
Howard S. Cohl , Loyal Durand
By starting with Durand's double integral representation for a product of two Jacobi functions of the second kind, we derive an integral representation for a product of two Jacobi functions of the second kind in kernel form. We also derive a Bateman-type sum for a product of two Jacobi functions of the second kind. From this integral representation we derive integral representations for the Jacobi function of the first kind in both the hyperbolic and trigonometric contexts. From the integral representations for Jacobi functions, we also derive integral representations for products of limiting functions such as associated Legendre functions of the first and second kind, Ferrers functions and also Gegenbauer functions of the first and second kind. By examining the behavior of one of these products near singularities of the relevant functions, we also derive integral representations for single functions, including a Laplace-type integral representation for the Jacobi function of the second kind. Finally, we use the product formulas for the functions of the second kind to derive Nicholson-type integral relations for the sums of squares of Jacobi functions of the first and second kinds, and in a confluent limit, Laguerre functions of the first and second kinds, which generalize the relation to those functions.
{"title":"Integral representation for a product of two Jacobi functions of the second kind","authors":"Howard S. Cohl , Loyal Durand","doi":"10.1016/j.jmaa.2026.130450","DOIUrl":"10.1016/j.jmaa.2026.130450","url":null,"abstract":"<div><div>By starting with Durand's double integral representation for a product of two Jacobi functions of the second kind, we derive an integral representation for a product of two Jacobi functions of the second kind in kernel form. We also derive a Bateman-type sum for a product of two Jacobi functions of the second kind. From this integral representation we derive integral representations for the Jacobi function of the first kind in both the hyperbolic and trigonometric contexts. From the integral representations for Jacobi functions, we also derive integral representations for products of limiting functions such as associated Legendre functions of the first and second kind, Ferrers functions and also Gegenbauer functions of the first and second kind. By examining the behavior of one of these products near singularities of the relevant functions, we also derive integral representations for single functions, including a Laplace-type integral representation for the Jacobi function of the second kind. Finally, we use the product formulas for the functions of the second kind to derive Nicholson-type integral relations for the sums of squares of Jacobi functions of the first and second kinds, and in a confluent limit, Laguerre functions of the first and second kinds, which generalize the relation <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mi>x</mi></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>i</mi><mi>x</mi></mrow></msup><mo>=</mo><mn>1</mn></math></span> to those functions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130450"},"PeriodicalIF":1.2,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-20DOI: 10.1016/j.jmaa.2026.130449
Lisbeth Carrero, Pedro Hernández-Llanos
<div><div>In this paper, we study the existence and nonexistence of solutions for the following Kirchhoff-type fractional <span><math><mo>(</mo><mi>p</mi><mtext>-</mtext><mi>q</mi><mo>)</mo></math></span>-Laplacian problem:<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mi>M</mi><mrow><mo>(</mo><msubsup><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow><mrow><mi>p</mi><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><mi>p</mi></mrow></msubsup><mo>)</mo></mrow><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msubsup><mi>u</mi><mo>+</mo><mi>M</mi><mrow><mo>(</mo><msubsup><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow><mrow><mi>q</mi><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><mi>q</mi></mrow></msubsup><mo>)</mo></mrow><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>q</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msubsup><mi>u</mi></mtd><mtd></mtd></mtr><mtr><mtd><mspace></mspace><mo>=</mo><mi>λ</mi><mo>[</mo><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>b</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>]</mo><mo>+</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo></mtd><mtd><mtext>in </mtext><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo></mtd><mtd><mtext>on </mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>∖</mo><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> where <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> (<span><math><mi>N</mi><mo>≥</mo><mn>1</mn></math></span>) is a bounded domain with smooth boundary, <span><math><mn>0</mn><mo><</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo><</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo><</mo><mn>1</mn></math></span>, and <span><math><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>p</mi><mo><</mo><mi>N</mi></math></span>. We assume <span><math><mn>1</mn><mo><</mo><mi>q</mi><mo>≤</mo><mi>p</mi><mo><</mo><mi>θ</mi><mi>p</mi><mo><</mo><msubsup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>:</mo><mo>=</mo><mfrac><mrow><mi>N</mi><mi>p</mi></mrow><mrow><mi>N</mi><mo>−</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>p</mi></mrow></mfrac></math></span>, and <span><math><mi>λ</mi><mo>∈</mo><mi>R</mi></math></span>. The functions <span><math><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>b</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>
{"title":"Kirchhoff-type equations involving the fractional (p,q)-Laplacian","authors":"Lisbeth Carrero, Pedro Hernández-Llanos","doi":"10.1016/j.jmaa.2026.130449","DOIUrl":"10.1016/j.jmaa.2026.130449","url":null,"abstract":"<div><div>In this paper, we study the existence and nonexistence of solutions for the following Kirchhoff-type fractional <span><math><mo>(</mo><mi>p</mi><mtext>-</mtext><mi>q</mi><mo>)</mo></math></span>-Laplacian problem:<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mi>M</mi><mrow><mo>(</mo><msubsup><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow><mrow><mi>p</mi><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><mi>p</mi></mrow></msubsup><mo>)</mo></mrow><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msubsup><mi>u</mi><mo>+</mo><mi>M</mi><mrow><mo>(</mo><msubsup><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow><mrow><mi>q</mi><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><mi>q</mi></mrow></msubsup><mo>)</mo></mrow><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>q</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msubsup><mi>u</mi></mtd><mtd></mtd></mtr><mtr><mtd><mspace></mspace><mo>=</mo><mi>λ</mi><mo>[</mo><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>b</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>]</mo><mo>+</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo></mtd><mtd><mtext>in </mtext><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo></mtd><mtd><mtext>on </mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>∖</mo><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> where <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> (<span><math><mi>N</mi><mo>≥</mo><mn>1</mn></math></span>) is a bounded domain with smooth boundary, <span><math><mn>0</mn><mo><</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo><</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo><</mo><mn>1</mn></math></span>, and <span><math><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>p</mi><mo><</mo><mi>N</mi></math></span>. We assume <span><math><mn>1</mn><mo><</mo><mi>q</mi><mo>≤</mo><mi>p</mi><mo><</mo><mi>θ</mi><mi>p</mi><mo><</mo><msubsup><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>:</mo><mo>=</mo><mfrac><mrow><mi>N</mi><mi>p</mi></mrow><mrow><mi>N</mi><mo>−</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>p</mi></mrow></mfrac></math></span>, and <span><math><mi>λ</mi><mo>∈</mo><mi>R</mi></math></span>. The functions <span><math><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>b</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130449"},"PeriodicalIF":1.2,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-20DOI: 10.1016/j.jmaa.2026.130447
Yanping Chen , Teng Wang , Huoxiong Wu
Let be a homogeneous function of degree zero and have mean value zero. Consider the rough singular integral We prove that is of weak type if the rough kernel function Ω belongs to the block space for some . This result substantially extends a classical theorem of Seeger (1996) [19].
{"title":"Weak type (1,1) bounds for singular integrals with rough kernels on block spaces","authors":"Yanping Chen , Teng Wang , Huoxiong Wu","doi":"10.1016/j.jmaa.2026.130447","DOIUrl":"10.1016/j.jmaa.2026.130447","url":null,"abstract":"<div><div>Let <span><math><mi>Ω</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></math></span> be a homogeneous function of degree zero and have mean value zero. Consider the rough singular integral<span><span><span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>Ω</mi></mrow></msub><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mrow><mi>p</mi><mo>.</mo><mi>v</mi><mo>.</mo></mrow><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></munder><mfrac><mrow><mi>Ω</mi><mo>(</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo>)</mo></mrow><mrow><mo>|</mo><mi>x</mi><mo>−</mo><mi>y</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>n</mi></mrow></msup></mrow></mfrac><mi>f</mi><mo>(</mo><mi>y</mi><mo>)</mo><mi>d</mi><mi>y</mi><mo>.</mo></math></span></span></span> We prove that <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>Ω</mi></mrow></msub></math></span> is of weak type <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> if the rough kernel function Ω belongs to the block space <span><math><msubsup><mrow><mi>B</mi></mrow><mrow><mi>q</mi></mrow><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></msubsup><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></math></span> for some <span><math><mi>q</mi><mo>></mo><mn>1</mn></math></span>. This result substantially extends a classical theorem of Seeger (1996) <span><span>[19]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130447"},"PeriodicalIF":1.2,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-19DOI: 10.1016/j.jmaa.2026.130443
Zuzana Došlá , Mauro Marini , Serena Matucci
A nonlinear differential equation with inhomogeneous differential operator Φ, which is regularly varying at zero, is considered. The operator Φ can be viewed as an extension of the p-Laplacian operator and arises in many physical problems, as illustrated by several examples. In particular, the existence of global positive bounded solutions on the half-line with the Neumann type boundary conditions is studied by means of an abstract fixed point theorem and certain properties of an associated half-linear equation. The results do not require the explicit form of the inverse operator of Φ, and are completed by an asymptotic analysis of these solutions near infinity.
{"title":"Global positive bounded solutions for equations with regularly varying operator","authors":"Zuzana Došlá , Mauro Marini , Serena Matucci","doi":"10.1016/j.jmaa.2026.130443","DOIUrl":"10.1016/j.jmaa.2026.130443","url":null,"abstract":"<div><div>A nonlinear differential equation with inhomogeneous differential operator Φ, which is regularly varying at zero, is considered. The operator Φ can be viewed as an extension of the <em>p</em>-Laplacian operator and arises in many physical problems, as illustrated by several examples. In particular, the existence of global positive bounded solutions on the half-line with the Neumann type boundary conditions is studied by means of an abstract fixed point theorem and certain properties of an associated half-linear equation. The results do not require the explicit form of the inverse operator of Φ, and are completed by an asymptotic analysis of these solutions near infinity.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130443"},"PeriodicalIF":1.2,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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