Pub Date : 2026-01-14DOI: 10.1016/j.jmaa.2026.130432
Lingli Hu , Zhaoyang Yin
In this paper, we prove the existence of the global conservative solutions of the two-component b-family equations by using the method in [3]. It is worth noting that we propose a new transformation method when transforming the original equation into a semilinear system.
{"title":"Global conservative solutions of a two-component b-family equations","authors":"Lingli Hu , Zhaoyang Yin","doi":"10.1016/j.jmaa.2026.130432","DOIUrl":"10.1016/j.jmaa.2026.130432","url":null,"abstract":"<div><div>In this paper, we prove the existence of the global conservative solutions of the two-component b-family equations by using the method in <span><span>[3]</span></span>. It is worth noting that we propose a new transformation method when transforming the original equation into a semilinear system.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130432"},"PeriodicalIF":1.2,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023488","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 : 2026-01-13DOI: 10.1016/j.jmaa.2026.130408
Ahmed Sebbar , Roger Gay
We study the singularities of the Dirichlet series when the power series has a singularity of general type at the point . This extends a recent result of L.M. Navas, J. Ruiz, and J.L. Varona, and connects to foundational ideas explored by Hardy, Fekete, and others. The tools employed include classical methods from the theory of Dirichlet series, particularly those often used in connection with the Riemann zeta function, namely the Mellin transform and splitting methods. These techniques were also used by Navas, Ruiz, and Varona. The polylogarithm function plays a fundamental role in this work.
当幂级数H(z)=∑n≥0hnzn在z0=1处具有一般型奇点时，研究了Dirichlet级数d (s)=∑n≥1hnns的奇异性。这扩展了L.M. Navas、J. Ruiz和J. l . Varona最近的研究结果，并与Hardy、Fekete等人探索的基本思想相联系。所使用的工具包括狄利克雷级数理论中的经典方法，特别是那些经常用于黎曼ζ函数的方法，即Mellin变换和分裂方法。Navas， Ruiz和Varona也使用了这些技术。多对数函数在这项工作中起着重要的作用。
{"title":"Dirichlet's series associated with some power series","authors":"Ahmed Sebbar , Roger Gay","doi":"10.1016/j.jmaa.2026.130408","DOIUrl":"10.1016/j.jmaa.2026.130408","url":null,"abstract":"<div><div>We study the singularities of the Dirichlet series<span><span><span><math><mi>D</mi><mo>(</mo><mi>s</mi><mo>)</mo><mo>=</mo><munder><mo>∑</mo><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></munder><mfrac><mrow><msub><mrow><mi>h</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow><mrow><msup><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msup></mrow></mfrac></math></span></span></span> when the power series <span><math><mi>H</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>=</mo><munder><mo>∑</mo><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></munder><msub><mrow><mi>h</mi></mrow><mrow><mi>n</mi></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> has a singularity of general type at the point <span><math><msub><mrow><mi>z</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>1</mn></math></span>. This extends a recent result of L.M. Navas, J. Ruiz, and J.L. Varona, and connects to foundational ideas explored by Hardy, Fekete, and others. The tools employed include classical methods from the theory of Dirichlet series, particularly those often used in connection with the Riemann zeta function, namely the Mellin transform and splitting methods. These techniques were also used by Navas, Ruiz, and Varona. The polylogarithm function plays a fundamental role in this work.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130408"},"PeriodicalIF":1.2,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023455","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 : 2026-01-13DOI: 10.1016/j.jmaa.2026.130415
Ohsang Kwon
We consider the following elliptic system which is motivated from Schrödinger equations where is the coupling constant, is sufficiently small constant, and is a potential function. We construct a solution in which one component exhibits a single peak at the origin, while the other component concentrates at the vertices of a regular tetrahedron. Existence of such a solution is obtained for all sufficiently small , highlighting that an arbitrarily small perturbation in the potential term of the second equation can induce a striking symmetry-breaking phenomenon. Our construction is achieved via a perturbative variational reduction method, which balances a central peak in U against multiple peripheral peaks in V in a highly symmetric configuration. These results extend the recent progress on segregated multi-peak solutions in coupled Schrödinger systems to a new three-dimensional symmetry pattern.
{"title":"On the existence for vector solutions of Schrödinger system with symmetry in tetrahedral group","authors":"Ohsang Kwon","doi":"10.1016/j.jmaa.2026.130415","DOIUrl":"10.1016/j.jmaa.2026.130415","url":null,"abstract":"<div><div>We consider the following elliptic system which is motivated from Schrödinger equations<span><span><span><math><mrow><mrow><mo>{</mo><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>U</mi><mo>+</mo><mi>U</mi><mo>=</mo><msup><mrow><mi>U</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><mi>α</mi><mi>U</mi><msup><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>V</mi><mo>+</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>ε</mi><mi>μ</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mi>V</mi><mo>=</mo><msup><mrow><mi>V</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><mi>α</mi><msup><mrow><mi>U</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>V</mi></mtd></mtr></mtable></mrow></mrow><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><mi>α</mi><mo>∈</mo><mi>R</mi></math></span> is the coupling constant, <span><math><mi>ε</mi><mo>></mo><mn>0</mn></math></span> is sufficiently small constant, and <span><math><mi>μ</mi><mo>:</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>→</mo><mi>R</mi></math></span> is a potential function. We construct a solution in which one component exhibits a single peak at the origin, while the other component concentrates at the vertices of a regular tetrahedron. Existence of such a solution is obtained for all sufficiently small <span><math><mi>ε</mi><mo>></mo><mn>0</mn></math></span>, highlighting that an arbitrarily small perturbation in the potential term of the second equation can induce a striking symmetry-breaking phenomenon. Our construction is achieved via a perturbative variational reduction method, which balances a central peak in <em>U</em> against multiple peripheral peaks in <em>V</em> in a highly symmetric configuration. These results extend the recent progress on segregated multi-peak solutions in coupled Schrödinger systems to a new three-dimensional symmetry pattern.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 2","pages":"Article 130415"},"PeriodicalIF":1.2,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023454","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 : 2026-01-13DOI: 10.1016/j.jmaa.2026.130412
Jaime E. Muñoz Rivera , Maria Grazia Naso , Bruna T. Silva Sozzo
We study the Euler-Bernoulli beam model with singularities at the points , and with localized viscoelastic dissipation of Kelvin-Voigt type. We assume that the beam is composed by two materials; one is an elastic material and the other one is a viscoelastic material of Kelvin-Voigt type.
Our main result is that the corresponding semigroup is immediately differentiable and also of Gevrey class 4. In particular, our result implies that the model is exponentially stable, has the linear stability property, and the smoothing effect property over the initial data.
{"title":"The Gevrey class of the Euler-Bernoulli beam model with singularities","authors":"Jaime E. Muñoz Rivera , Maria Grazia Naso , Bruna T. Silva Sozzo","doi":"10.1016/j.jmaa.2026.130412","DOIUrl":"10.1016/j.jmaa.2026.130412","url":null,"abstract":"<div><div>We study the Euler-Bernoulli beam model with singularities at the points <span><math><mi>x</mi><mo>=</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, <span><math><mi>x</mi><mo>=</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and with localized viscoelastic dissipation of Kelvin-Voigt type. We assume that the beam is composed by two materials; one is an elastic material and the other one is a viscoelastic material of Kelvin-Voigt type.</div><div>Our main result is that the corresponding semigroup is immediately differentiable and also of Gevrey class 4. In particular, our result implies that the model is exponentially stable, has the linear stability property, and the smoothing effect property over the initial data.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130412"},"PeriodicalIF":1.2,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981213","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 : 2026-01-13DOI: 10.1016/j.jmaa.2026.130407
Han-Su Zhang, Biyue Chen, Renxiang Shi
In this paper we investigate an indefinite nonlinear Schrödinger system with steep potential well in . By exploiting the relationship between the Nehari manifold and fibering maps, we reveal how the Nehari manifold changes as the two parameters vary, and eventually establish the existence and multiplicity of positive solutions.
{"title":"Existence and multiplicity of positive solutions for an indefinite nonlinear Schrödinger system in RN","authors":"Han-Su Zhang, Biyue Chen, Renxiang Shi","doi":"10.1016/j.jmaa.2026.130407","DOIUrl":"10.1016/j.jmaa.2026.130407","url":null,"abstract":"<div><div>In this paper we investigate an indefinite nonlinear Schrödinger system with steep potential well in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>. By exploiting the relationship between the Nehari manifold and fibering maps, we reveal how the Nehari manifold changes as the two parameters vary, and eventually establish the existence and multiplicity of positive solutions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130407"},"PeriodicalIF":1.2,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024439","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 : 2026-01-12DOI: 10.1016/j.jmaa.2026.130400
Ziheng Song
An error occurs in the paper “Hausdorff dimension of some sets in the theory of continued beta-fractions and its generalized continued fractions” [J. Math. Anal. Appl. 535 (2024) 128120] and it is corrected in this corrigendum.
{"title":"Corrigendum to “Hausdorff dimension of some sets in the theory of continued beta-fractions and its generalized continued fractions” [J. Math. Anal. Appl. 535 (2024) 128120]","authors":"Ziheng Song","doi":"10.1016/j.jmaa.2026.130400","DOIUrl":"10.1016/j.jmaa.2026.130400","url":null,"abstract":"<div><div>An error occurs in the paper <em>“Hausdorff dimension of some sets in the theory of continued beta-fractions and its generalized continued fractions”</em> [J. Math. Anal. Appl. 535 (2024) 128120] and it is corrected in this corrigendum.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"557 1","pages":"Article 130400"},"PeriodicalIF":1.2,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145977130","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.2026.130405
Laurent Cantier
This paper investigates and classifies a specific class of one-parameter continuous fields of -algebras, which can be seen as generalized AI-algebras. Building on the classification of *-homomorphisms between interval algebras by the Cuntz semigroup, along with a selection theorem and a gluing procedure, we employ a ‘local-to-global’ strategy to achieve our classification result.
{"title":"Continuous fields of interval algebras","authors":"Laurent Cantier","doi":"10.1016/j.jmaa.2026.130405","DOIUrl":"10.1016/j.jmaa.2026.130405","url":null,"abstract":"<div><div>This paper investigates and classifies a specific class of one-parameter continuous fields of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebras, which can be seen as generalized AI-algebras. Building on the classification of *-homomorphisms between interval algebras by the Cuntz semigroup, along with a selection theorem and a gluing procedure, we employ a ‘local-to-global’ strategy to achieve our classification result.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130405"},"PeriodicalIF":1.2,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978197","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.2026.130402
Tao Cheng , Yan Wu , Haoran Zou
We construct the pre-Schwarzian derivative space of harmonic mappings and investigate its topological connectedness. Furthermore, we show that the interior of contains the model of the universal Teichmüller space embedded by pre-Schwarzian derivative.
{"title":"Topological structure of the pre-Schwarzian derivative space of harmonic mappings","authors":"Tao Cheng , Yan Wu , Haoran Zou","doi":"10.1016/j.jmaa.2026.130402","DOIUrl":"10.1016/j.jmaa.2026.130402","url":null,"abstract":"<div><div>We construct the pre-Schwarzian derivative space <span><math><mi>H</mi></math></span> of harmonic mappings and investigate its topological connectedness. Furthermore, we show that the interior of <span><math><mi>H</mi></math></span> contains the model of the universal Teichmüller space embedded by pre-Schwarzian derivative.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130402"},"PeriodicalIF":1.2,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981838","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.2026.130404
Andrew Fiori
We provide a generalization of the Phragmén-Lindelöf principal of Rademacher with the aim of correcting, or at least provide a pathway to correcting, several errors appearing in the literature.
{"title":"A note on the Phragmén-Lindelöf theorem","authors":"Andrew Fiori","doi":"10.1016/j.jmaa.2026.130404","DOIUrl":"10.1016/j.jmaa.2026.130404","url":null,"abstract":"<div><div>We provide a generalization of the Phragmén-Lindelöf principal of Rademacher with the aim of correcting, or at least provide a pathway to correcting, several errors appearing in the literature.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130404"},"PeriodicalIF":1.2,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981839","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.2026.130392
Oscar A.R. Cespedes , Rony Cristiano , Otávio M.L. Gomide
This paper investigates the local behavior of 3D Filippov systems , focusing on the dynamics around cusp-fold singularities. These singular points, characterized by cubic contact of vector field X and quadratic contact of vector field Y on the switching manifold, are structurally unstable under small perturbations of Z, giving rise to significant bifurcation phenomena.
We analyze the bifurcations of a 3D Filippov system around an invisible cusp-fold singularity, providing a detailed characterization of its crossing dynamics under certain conditions. We classify the characteristics of the singularity when it emerges generically in one-parameter families (a codimension-one phenomenon), and we show that no crossing limit cycles (CLCs) locally bifurcate from it in this particular scenario. When the vector fields X and Y are anti-collinear at the cusp-fold singularity, we provide conditions for the generic emergence of this point in two-parameter families (a codimension-two phenomenon). In this case, we show that the unfolding of such a singularity leads to a bifurcating CLC, which degenerates into a fold-regular polycycle (self-connection at a fold-regular singularity).
Furthermore, we numerically derive the polycycle bifurcation curve and complete the two-parameter bifurcation set for a boost converter system previously studied in the literature. This allows the identification of parameter regions where the boost converter system exhibits a CLC in its phase portrait, providing a understanding of its complex dynamics.
{"title":"Bifurcation analysis of 3D-Filippov systems around Cusp-Fold singularities","authors":"Oscar A.R. Cespedes , Rony Cristiano , Otávio M.L. Gomide","doi":"10.1016/j.jmaa.2026.130392","DOIUrl":"10.1016/j.jmaa.2026.130392","url":null,"abstract":"<div><div>This paper investigates the local behavior of 3D Filippov systems <span><math><mi>Z</mi><mo>=</mo><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></math></span>, focusing on the dynamics around cusp-fold singularities. These singular points, characterized by cubic contact of vector field <em>X</em> and quadratic contact of vector field <em>Y</em> on the switching manifold, are structurally unstable under small perturbations of <em>Z</em>, giving rise to significant bifurcation phenomena.</div><div>We analyze the bifurcations of a 3D Filippov system around an invisible cusp-fold singularity, providing a detailed characterization of its crossing dynamics under certain conditions. We classify the characteristics of the singularity when it emerges generically in one-parameter families (a codimension-one phenomenon), and we show that no crossing limit cycles (CLCs) locally bifurcate from it in this particular scenario. When the vector fields <em>X</em> and <em>Y</em> are anti-collinear at the cusp-fold singularity, we provide conditions for the generic emergence of this point in two-parameter families (a codimension-two phenomenon). In this case, we show that the unfolding of such a singularity leads to a bifurcating CLC, which degenerates into a fold-regular polycycle (self-connection at a fold-regular singularity).</div><div>Furthermore, we numerically derive the polycycle bifurcation curve and complete the two-parameter bifurcation set for a boost converter system previously studied in the literature. This allows the identification of parameter regions where the boost converter system exhibits a CLC in its phase portrait, providing a understanding of its complex dynamics.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130392"},"PeriodicalIF":1.2,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024443","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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