Pub Date : 2026-01-09DOI: 10.1016/j.jmaa.2026.130403
Thai Duong Do , Ngoc Thanh Cong Pham
In this paper, we study the non-pluripolar complex Monge-Ampère measure on bounded domains in . We establish a general existence theorem for a non-pluripolar complex Monge-Ampère type equation with prescribed singularity on a bounded hyperconvex domain in .
{"title":"An existence theorem for non-pluripolar complex Monge-Ampère type equations on hyperconvex domains","authors":"Thai Duong Do , Ngoc Thanh Cong Pham","doi":"10.1016/j.jmaa.2026.130403","DOIUrl":"10.1016/j.jmaa.2026.130403","url":null,"abstract":"<div><div>In this paper, we study the non-pluripolar complex Monge-Ampère measure on bounded domains in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. We establish a general existence theorem for a non-pluripolar complex Monge-Ampère type equation with prescribed singularity on a bounded hyperconvex domain in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130403"},"PeriodicalIF":1.2,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981212","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 : 2026-01-09DOI: 10.1016/j.jmaa.2026.130398
Andreas Mono
In 2003, Pei and Wang introduced higher level analogs of the classical Cohen–Eisenstein series. In recent joint work with Beckwith, we found a weight sesquiharmonic preimage of their weight Eisenstein series under utilizing a construction from seminal work by Duke, Imamoḡlu and Tóth. In further joint work with Beckwith, when restricting to prime level, we realized our preimage as a regularized Siegel theta lift and evaluated its (regularized) Fourier coefficients explicitly. This relied crucially on work by Bruinier, Funke and Imamoḡlu. In this paper, we extend both works to higher weights. That is, we provide a harmonic preimage of Pei and Wang's generalized Cohen–Eisenstein series under , where . Furthermore, when restricting to prime level, we realize them as outputs of a regularized Shintani theta lift of a higher level holomorphic Eisenstein series, which builds on recent work by Alfes and Schwagenscheidt. Lastly, we evaluate the regularized Millson theta lift of a higher level Maass–Eisenstein series, which is known to be connected to the Shintani theta lift by a differential equation by earlier work of Alfes and Schwagenscheidt.
{"title":"A modular framework for generalized Hurwitz class numbers III","authors":"Andreas Mono","doi":"10.1016/j.jmaa.2026.130398","DOIUrl":"10.1016/j.jmaa.2026.130398","url":null,"abstract":"<div><div>In 2003, Pei and Wang introduced higher level analogs of the classical Cohen–Eisenstein series. In recent joint work with Beckwith, we found a weight <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> sesquiharmonic preimage of their weight <span><math><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> Eisenstein series under <span><math><msub><mrow><mi>ξ</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msub></math></span> utilizing a construction from seminal work by Duke, Imamoḡlu and Tóth. In further joint work with Beckwith, when restricting to prime level, we realized our preimage as a regularized Siegel theta lift and evaluated its (regularized) Fourier coefficients explicitly. This relied crucially on work by Bruinier, Funke and Imamoḡlu. In this paper, we extend both works to higher weights. That is, we provide a harmonic preimage of Pei and Wang's generalized Cohen–Eisenstein series under <span><math><msub><mrow><mi>ξ</mi></mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mi>k</mi></mrow></msub></math></span>, where <span><math><mi>k</mi><mo>></mo><mn>1</mn></math></span>. Furthermore, when restricting to prime level, we realize them as outputs of a regularized Shintani theta lift of a higher level holomorphic Eisenstein series, which builds on recent work by Alfes and Schwagenscheidt. Lastly, we evaluate the regularized Millson theta lift of a higher level Maass–Eisenstein series, which is known to be connected to the Shintani theta lift by a differential equation by earlier work of Alfes and Schwagenscheidt.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130398"},"PeriodicalIF":1.2,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981211","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 : 2026-01-08DOI: 10.1016/j.jmaa.2026.130397
William L. Blair
We extend representation formulas for functions in Hardy classes of solutions to higher-order iterated Vekua equations to Hardy classes of bicomplex-valued functions that solve a bicomplex version of the Vekua equation or its higher-order generalizations. Using these representations, we show that functions in these bicomplex-valued Hardy classes have nontangential boundary values and boundary values in the sense of distributions.
{"title":"Bicomplex Hardy classes of solutions to higher-order Vekua equations","authors":"William L. Blair","doi":"10.1016/j.jmaa.2026.130397","DOIUrl":"10.1016/j.jmaa.2026.130397","url":null,"abstract":"<div><div>We extend representation formulas for functions in Hardy classes of solutions to higher-order iterated Vekua equations to Hardy classes of bicomplex-valued functions that solve a bicomplex version of the Vekua equation or its higher-order generalizations. Using these representations, we show that functions in these bicomplex-valued Hardy classes have nontangential boundary values and boundary values in the sense of distributions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130397"},"PeriodicalIF":1.2,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978788","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 : 2026-01-08DOI: 10.1016/j.jmaa.2026.130401
Chenglin Geng, Jiawei Xiong
In this paper, we focus on solving the logarithmic Minkowski problem for triangular frustums in 3-dimensional Euclidean space. It investigates the necessary and sufficient conditions for a discrete measure on the unit sphere to be the cone-volume measure of a triangular frustum containing the origin. The main result shows that such a measure exists if and only if there exists a specific real number η within satisfying a certain polynomial relation involving the measure's components. Additionally, the paper demonstrates the non-uniqueness of solutions to this problem through construction and verification.
{"title":"The logarithmic Minkowski problem for triangular frustum","authors":"Chenglin Geng, Jiawei Xiong","doi":"10.1016/j.jmaa.2026.130401","DOIUrl":"10.1016/j.jmaa.2026.130401","url":null,"abstract":"<div><div>In this paper, we focus on solving the logarithmic Minkowski problem for triangular frustums in 3-dimensional Euclidean space. It investigates the necessary and sufficient conditions for a discrete measure on the unit sphere to be the cone-volume measure of a triangular frustum containing the origin. The main result shows that such a measure exists if and only if there exists a specific real number <em>η</em> within <span><math><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> satisfying a certain polynomial relation involving the measure's components. Additionally, the paper demonstrates the non-uniqueness of solutions to this problem through construction and verification.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130401"},"PeriodicalIF":1.2,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145950330","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 : 2026-01-08DOI: 10.1016/j.jmaa.2026.130406
Xiong Lin, Jianfei Wang
We establish the Holland-Walsh-Zhao characterization of Bloch-type spaces defined on a general convex domain in one and higher dimensions, respectively. Firstly, by using the concavity with hyperbolic metric on a plane convex domain, we extend the Holland-Walsh-Zhao criterium for the membership of Bloch-type spaces from the unit disk to the plane convex domain. Secondly, we generalize the higher dimensional Holland-Walsh-Zhao characterization of the weighted Bloch-type spaces with some concavity weight. Thirdly, a new characterization of Bloch space of the unit ball in is obtained by proving certain estimates of Kobayashi distance of the unit ball, which improves the Nowak and Ren-Tu characterization of Bloch space. Finally, we apply the Holland-Walsh characterization to prove that the Roper-Suffridge extension operator preserves Bloch property, which generalizes many well-known results.
{"title":"On the generalized Holland-Walsh-Zhao characterization of Bloch-type spaces","authors":"Xiong Lin, Jianfei Wang","doi":"10.1016/j.jmaa.2026.130406","DOIUrl":"10.1016/j.jmaa.2026.130406","url":null,"abstract":"<div><div>We establish the Holland-Walsh-Zhao characterization of Bloch-type spaces defined on a general convex domain in one and higher dimensions, respectively. Firstly, by using the concavity with hyperbolic metric on a plane convex domain, we extend the Holland-Walsh-Zhao criterium for the membership of Bloch-type spaces from the unit disk to the plane convex domain. Secondly, we generalize the higher dimensional Holland-Walsh-Zhao characterization of the weighted Bloch-type spaces with some concavity weight. Thirdly, a new characterization of Bloch space of the unit ball in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is obtained by proving certain estimates of Kobayashi distance of the unit ball, which improves the Nowak and Ren-Tu characterization of Bloch space. Finally, we apply the Holland-Walsh characterization to prove that the Roper-Suffridge extension operator preserves Bloch property, which generalizes many well-known results.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130406"},"PeriodicalIF":1.2,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981836","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 : 2026-01-08DOI: 10.1016/j.jmaa.2026.130394
Xiao-Dong Cao , Chao-Jiang Xu , Yan Xu
We focus on the spatially homogeneous Landau equation with soft potential under the perturbation framework to the global equilibrium. By induction, we achieve time analyticity and the Gelfand-Shilov regularizing effect for the velocity variables, so that for the Cauchy problem with initial datum, we gain the exponential moments production and Gevrey smoothing effects.
{"title":"Regularizing effect of the spatially homogeneous Landau equation with soft potential","authors":"Xiao-Dong Cao , Chao-Jiang Xu , Yan Xu","doi":"10.1016/j.jmaa.2026.130394","DOIUrl":"10.1016/j.jmaa.2026.130394","url":null,"abstract":"<div><div>We focus on the spatially homogeneous Landau equation with soft potential under the perturbation framework to the global equilibrium. By induction, we achieve time analyticity and the Gelfand-Shilov regularizing effect for the velocity variables, so that for the Cauchy problem with <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> initial datum, we gain the exponential moments production and Gevrey smoothing effects.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"557 2","pages":"Article 130394"},"PeriodicalIF":1.2,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145977427","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 : 2026-01-08DOI: 10.1016/j.jmaa.2026.130395
Franck Boyer , Michel Fournié , Diego Gajardo , Jean-Pierre Raymond
In this paper, we consider the stationary Stokes system with mixed boundary conditions, of Dirichlet and Neumann types, in a bounded non-convex curvilinear polygonal domain of . We prove, in particular, a precise regularity result in heterogeneous Sobolev spaces taking into account the fact that the expected regularity is of different nature near the corners of the domain and near the Dirichlet-Neumann transition points. Then, we prove the analyticity of the semigroup generated by the Stokes operator in an appropriate functional setting. We also give a characterization of the stationary Stokes system as an operator equation. Those results, that can be useful in various situations, are in particular motivated by the analysis of a fluid-structure interaction system investigated by the authors in a forthcoming paper, and for which they represent an essential step.
{"title":"Study of the stationary Stokes system with mixed boundary conditions in non-convex curvilinear polygonal domains","authors":"Franck Boyer , Michel Fournié , Diego Gajardo , Jean-Pierre Raymond","doi":"10.1016/j.jmaa.2026.130395","DOIUrl":"10.1016/j.jmaa.2026.130395","url":null,"abstract":"<div><div>In this paper, we consider the stationary Stokes system with mixed boundary conditions, of Dirichlet and Neumann types, in a bounded non-convex curvilinear polygonal domain of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. We prove, in particular, a precise regularity result in heterogeneous Sobolev spaces taking into account the fact that the expected regularity is of different nature near the corners of the domain and near the Dirichlet-Neumann transition points. Then, we prove the analyticity of the semigroup generated by the Stokes operator in an appropriate functional setting. We also give a characterization of the stationary Stokes system as an operator equation. Those results, that can be useful in various situations, are in particular motivated by the analysis of a fluid-structure interaction system investigated by the authors in a forthcoming paper, and for which they represent an essential step.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130395"},"PeriodicalIF":1.2,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978195","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 : 2026-01-08DOI: 10.1016/j.jmaa.2026.130390
Angelica Pia Di Feola, Vittorio Pane
We investigate the initial-boundary value problem for the Stokes system in the halfspace, within the framework of weighted Lebesgue spaces. Introducing a new weight function defined via a product of powers of distances from fixed points, we establish existence, uniqueness, and regularity results for strong solutions to the Stokes problem in the half space. Our analysis generalizes previous results for the Stokes system in radial-weighted spaces (Galdi and Maremonti, 2023 [9]; Maremonti and Pane, 2025 [17]) and extends the theory to our setting. Moreover, we give the space-time behavior of the solution. These results represent a first step toward the analysis of the Navier-Stokes system in weighted spaces, with applications in both half-space and exterior domain configurations.
{"title":"Weighted estimates for the Stokes semigroup in the half-space","authors":"Angelica Pia Di Feola, Vittorio Pane","doi":"10.1016/j.jmaa.2026.130390","DOIUrl":"10.1016/j.jmaa.2026.130390","url":null,"abstract":"<div><div>We investigate the initial-boundary value problem for the Stokes system in the halfspace, within the framework of weighted Lebesgue spaces. Introducing a new weight function defined via a product of powers of distances from fixed points, we establish existence, uniqueness, and regularity results for strong solutions to the Stokes problem in the half space. Our analysis generalizes previous results for the Stokes system in radial-weighted spaces (Galdi and Maremonti, 2023 <span><span>[9]</span></span>; Maremonti and Pane, 2025 <span><span>[17]</span></span>) and extends the theory to our setting. Moreover, we give the space-time behavior of the solution. These results represent a first step toward the analysis of the Navier-Stokes system in weighted spaces, with applications in both half-space and exterior domain configurations.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130390"},"PeriodicalIF":1.2,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023456","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}
We prove that local stable/unstable sets of homeomorphisms of an infinite compact metric space satisfying the gluing-orbit property always contain compact and perfect subsets of the space. As a consequence, we prove that if a positively countably expansive homeomorphism satisfies the gluing-orbit property, then the space is a single periodic orbit. We also prove that there are homeomorphisms with gluing-orbit such that its induced homeomorphism on the hyperspace of compact subsets does not have gluing-orbit, contrasting with the case of the shadowing and specification properties, proving that if the induced map has gluing-orbit, then the base map has gluing-orbit and is topologically mixing.
{"title":"Gluing-orbit property, local stable/unstable sets, and induced dynamics on hyperspace","authors":"Mayara Antunes , Bernardo Carvalho , Welington Cordeiro , José Cueto","doi":"10.1016/j.jmaa.2026.130389","DOIUrl":"10.1016/j.jmaa.2026.130389","url":null,"abstract":"<div><div>We prove that local stable/unstable sets of homeomorphisms of an infinite compact metric space satisfying the gluing-orbit property always contain compact and perfect subsets of the space. As a consequence, we prove that if a positively countably expansive homeomorphism satisfies the gluing-orbit property, then the space is a single periodic orbit. We also prove that there are homeomorphisms with gluing-orbit such that its induced homeomorphism on the hyperspace of compact subsets does not have gluing-orbit, contrasting with the case of the shadowing and specification properties, proving that if the induced map has gluing-orbit, then the base map has gluing-orbit and is topologically mixing.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130389"},"PeriodicalIF":1.2,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939668","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 : 2026-01-07DOI: 10.1016/j.jmaa.2026.130396
Zhijun Zhang
This paper is mainly concerned with the global and boundary asymptotic behavior of convex large classical solutions to the Monge-Ampère equation , , where Ω is a strictly convex and bounded smooth domain in with , , with , or , and with for some and . We completely describe how and ∂Ω affect the asymptotic behavior of solutions to such problem.
{"title":"Asymptotic behavior of large solutions to a class of Monge-Ampère equations with nonlinear gradient terms","authors":"Zhijun Zhang","doi":"10.1016/j.jmaa.2026.130396","DOIUrl":"10.1016/j.jmaa.2026.130396","url":null,"abstract":"<div><div>This paper is mainly concerned with the global and boundary asymptotic behavior of convex large classical solutions to the Monge-Ampère equation <span><math><mrow><mi>det</mi></mrow><mspace></mspace><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>f</mi><mo>(</mo><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>+</mo><mi>b</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo><mi>∇</mi><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi></mrow></msup></math></span>, <span><math><mi>x</mi><mo>∈</mo><mi>Ω</mi></math></span>, where Ω is a strictly convex and bounded smooth domain in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>, <span><math><mi>q</mi><mo>></mo><mn>0</mn></math></span>, <span><math><mi>f</mi><mo>(</mo><mi>s</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>s</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> with <span><math><mi>p</mi><mo>></mo><mn>0</mn></math></span>, or <span><math><mi>f</mi><mo>(</mo><mi>s</mi><mo>)</mo><mo>=</mo><mi>exp</mi><mo></mo><mi>s</mi></math></span>, and <span><math><mi>b</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> with <span><math><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mi>d</mi></mrow><mrow><mi>α</mi></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>≤</mo><mi>b</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≤</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mi>d</mi></mrow><mrow><mi>α</mi></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mspace></mspace><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi></math></span> for some <span><math><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>></mo><mn>0</mn></math></span> and <span><math><mi>α</mi><mo>≥</mo><mi>q</mi><mo>−</mo><mi>n</mi><mo>−</mo><mn>1</mn></math></span>. We completely describe how <span><math><mi>n</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>,</mo><mi>α</mi></math></span> and ∂Ω affect the asymptotic behavior of solutions to such problem.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130396"},"PeriodicalIF":1.2,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939667","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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