Journal of Mathematical Analysis and Applications最新文献

{"title":"Multiplicative partial isometries, manageability, and C⁎-algebraic quantum groupoids","authors":"Byung-Jay Kahng","doi":"10.1016/j.jmaa.2026.130535","DOIUrl":"10.1016/j.jmaa.2026.130535","url":null,"abstract":"<div><div>Generalizing the notion of a multiplicative unitary operator, which plays a fundamental role in the theory of locally compact quantum groups, we develop in this paper the notion of a <em>multiplicative partial isometry</em>. The axioms include the pentagon equation, but more is needed. Under the “manageability” condition on a multiplicative partial isometry (modified from the Woronowicz's condition for a multiplicative unitary), it is possible to construct from it a pair of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebras having almost the structure of a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span><em>-algebraic quantum groupoid of separable type</em>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130535"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385483","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}

{"title":"Local energy decay for 2-D wave equations with variable coefficients","authors":"Ryo Ikehata","doi":"10.1016/j.jmaa.2026.130554","DOIUrl":"10.1016/j.jmaa.2026.130554","url":null,"abstract":"<div><div>This paper addresses the two-dimensional initial value problem in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> for the wave equation with varying spatial coefficients in the main part. Assuming compactness in the support of the initial value, we report that the corresponding local energy decays to an order of magnitude of, for example, <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><msqrt><mrow><mi>log</mi><mo>⁡</mo><mi>t</mi></mrow></msqrt><mo>)</mo></math></span> after sufficiently large time. For the two-dimensional whole space case, it is crucial to establish the optimal <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-estimate for the solution itself, skillfully avoiding the difficulty of not being able to use useful inequalities such as Hardy-type inequalities in higher dimensional case. We also consider cases where the variable coefficients are slightly generalized. These proofs are developed using the multiplier method.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130554"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385484","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}

{"title":"On the rate of growth of Bessel–Fourier coefficients for integrable functions","authors":"Ryan L. Acosta Babb","doi":"10.1016/j.jmaa.2026.130440","DOIUrl":"10.1016/j.jmaa.2026.130440","url":null,"abstract":"<div><div>It is known that the Bessel–Fourier coefficients <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow></msub></math></span> of a function <em>f</em>, such that <span><math><msup><mrow><mi>x</mi></mrow><mrow><mi>s</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is integrable over <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> with <span><math><mn>0</mn><mo>⩽</mo><mi>s</mi><mo>⩽</mo><mi>ν</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span>, satisfy <span><math><msubsup><mrow><mi>j</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow><mrow><mo>−</mo><mi>s</mi><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msubsup><msub><mrow><mi>f</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow></msub><mo>→</mo><mn>0</mn></math></span>. We show a partial converse, namely that for <span><math><mn>0</mn><mo>⩽</mo><mi>α</mi><mo>&lt;</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span> and any non-negative <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>→</mo><mn>0</mn></math></span>, there is a function <em>f</em> such that <span><math><msup><mrow><mi>x</mi></mrow><mrow><mi>α</mi><mo>+</mo><mn>1</mn><mo>+</mo><mi>ν</mi></mrow></msup><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is integrable and its Bessel–Fourier coefficients <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow></msub></math></span> satisfy <span><math><msubsup><mrow><mi>j</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msubsup><msub><mrow><mi>f</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow></msub><mo>⩾</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> and <span><math><msubsup><mrow><mi>j</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msubsup><msub><mrow><mi>f</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow></msub><mo>→</mo><mn>0</mn></math></span>. For <span><math><mi>ν</mi><mo>=</mo><mn>0</mn></math></span>, we conjecture that the same should be true when <span><math><mi>α</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>, and discuss some consequences of this conjecture for the divergence Bessel–Fourier expansions of radial functions on the disc.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130440"},"PeriodicalIF":1.2,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024435","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}

{"title":"Dirichlet problem for diffusions with jumps","authors":"Zhen-Qing Chen ,&nbsp;Jun Peng","doi":"10.1016/j.jmaa.2025.130386","DOIUrl":"10.1016/j.jmaa.2025.130386","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper, we study Dirichlet problem on bounded open sets in &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; for non-local operators of the following form&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;div&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is a measurable &lt;span&gt;&lt;math&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; matrix-valued function on &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; that is uniformly elliptic and bounded, &lt;em&gt;b&lt;/em&gt; is an &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;-valued function so that &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; is in some Kato class &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is a finite measure on &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; for each &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; so that &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;↦&lt;/mo&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is in the Kato class &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. We show there is a unique Feller process &lt;em&gt;X&lt;/em&gt; having strong Feller property associated with &lt;span&gt;&lt;math&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, which can be obtained from the diffusion process having generator &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;div&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; through redistribution. We further show that for any bounded connected open subset &lt;span&gt;&lt;math&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; that is regular with respect to ","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130386"},"PeriodicalIF":1.2,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981214","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}

{"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":"2026-07-01","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}

{"title":"Topological structure of the pre-Schwarzian derivative space of harmonic mappings","authors":"Tao Cheng ,&nbsp;Yan Wu ,&nbsp;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":"2026-07-01","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}

{"title":"A dynamic thermo-mechanical system with Signorini's complementarity condition and Barber's boundary heat-exchange condition","authors":"L. Paoli ,&nbsp;M. Shillor","doi":"10.1016/j.jmaa.2026.130434","DOIUrl":"10.1016/j.jmaa.2026.130434","url":null,"abstract":"<div><div>This work is motivated by recent developments in MEMS devices, such as actuators and grippers. It analyzes the dynamics of a thermo-mechanical system, which can be found in most MEMS, consisting of a vertical rod joined at one end to a horizontal beam. The thermal expansion or vibration of the rod may cause the other end to come into contact with another device, the <em>obstacle</em>. This contact closes an electrical circuit, which is the actuating or switching function of such MEMS. The interaction between the rod's contacting end and the obstacle is described by Signorini's non-penetration contact condition for the displacements and by an inclusion-type Barber's heat exchange condition for the temperature. The heat-exchange coefficient is assumed to be a multi-function taking into account the air resistance in the gap. Moreover, the beam and the rod are assumed to be purely elastic. The model consists of a non-linear variational inclusion for the temperature coupled with a non-linear variational inequality for the displacements. To show the existence of a weak solution to the problem, we introduce a sequence of approximate problems, by considering a regularization of both Signorini's and Barber's conditions. We establish the existence of solutions to the approximate problems and then prove the convergence of these approximate solutions, as the regularization parameters vanish, to a solution of the original problem.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130434"},"PeriodicalIF":1.2,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024441","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}

{"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":"2026-07-01","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}

{"title":"Bifurcation analysis of 3D-Filippov systems around Cusp-Fold singularities","authors":"Oscar A.R. Cespedes ,&nbsp;Rony Cristiano ,&nbsp;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":"2026-07-01","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}

{"title":"The Hutchinson-Barnsley theory for iterated function systems with general measures","authors":"Elismar R. Oliveira ,&nbsp;Rafael R. Souza","doi":"10.1016/j.jmaa.2026.130456","DOIUrl":"10.1016/j.jmaa.2026.130456","url":null,"abstract":"<div><div>In this work we present iterated function systems with general measures (IFSm) formed by a set of maps <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> acting on a compact space <em>X</em>, for a compact space of indices, Λ. The Markov process <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> associated with the IFS iteration is defined using a general family of probability measures <span><math><msub><mrow><mi>q</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span> on Λ, where <span><math><mi>x</mi><mo>∈</mo><mi>X</mi></math></span>: <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span> is given by <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></math></span>, with <em>λ</em> randomly chosen according to <span><math><msub><mrow><mi>q</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span>. We prove the existence of the topological attractor and the existence of the invariant attracting measure for the Markov Process. We also prove that the support of the invariant measure is given by the attractor and results on the stochastic stability of the invariant measures, with respect to changes in the family <span><math><msub><mrow><mi>q</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130456"},"PeriodicalIF":1.2,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079639","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}