Nonlinear Analysis-Real World Applications最新文献

{"title":"Global strong solutions to the 3D nonhomogeneous incompressible magneto-micropolar fluid equations with density-dependent viscosity","authors":"Xia Ye ,&nbsp;Yue Zhou ,&nbsp;Mingxuan Zhu","doi":"10.1016/j.nonrwa.2025.104477","DOIUrl":"10.1016/j.nonrwa.2025.104477","url":null,"abstract":"<div><div>This paper concerns the Cauchy problem for magneto-micropolar fluid equations with density-dependent viscosity in the entire space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. By utilizing some crucial decay-in-time estimates, we establish the global existence and uniqueness of strong solutions, provided that the initial velocity is suitably small, without requiring smallness of the initial density.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104477"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830107","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":"Global stability of perturbed chemostat systems","authors":"Claudia Alvarez-Latuz ,&nbsp;Térence Bayen ,&nbsp;Jérôme Coville","doi":"10.1016/j.nonrwa.2025.104509","DOIUrl":"10.1016/j.nonrwa.2025.104509","url":null,"abstract":"<div><div>This paper is devoted to the analysis of the global stability of the chemostat system with a perturbation term representing a general form of exchange between species. This conversion term depends not only on species and substrate concentrations, but also on a positive perturbation parameter. After expressing the invariant manifold as a union of a family of compact subsets, our main result states that for each subset in this family, there exists a positive threshold for the perturbation parameter below which the system is globally asymptotically stable in the corresponding subset. Our approach relies on the Malkin-Gorshin Theorem and on a Theorem by Smith and Waltman concerning perturbations of a globally stable steady-state. Properties of the steady-states and numerical simulations of the system’s asymptotic behavior complement this study for two types of perturbation terms between the species.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104509"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145117683","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":"Exponential stability for an infinite memory wave equation with frictional damping and logarithmic nonlinear terms","authors":"Qingqing Peng ,&nbsp;Yikan Liu","doi":"10.1016/j.nonrwa.2025.104470","DOIUrl":"10.1016/j.nonrwa.2025.104470","url":null,"abstract":"<div><div>This article is concerned with the energy decay of an infinite memory wave equation with a logarithmic nonlinear term and a frictional damping term. The problem is formulated in a bounded domain in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> (<span><math><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></math></span>) with a smooth boundary, on which we prescribe a mixed boundary condition of the Dirichlet and the acoustic types. We establish an exponential decay result for the energy with a general material density <span><math><mrow><mi>ρ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> under certain assumptions on the involved coefficients. The proof is based on a contradiction argument, the multiplier method and some microlocal analysis techniques. In addition, if <span><math><mrow><mi>ρ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> takes a special form, our result even holds without the damping effect, that is, the infinite memory effect alone is strong enough to guarantee the exponential stability of the system.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104470"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144780442","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 p-Laplacian heat equation in a non-cylindrical domain with an oscillating boundary: A homogenization process","authors":"Akambadath Keerthiyil Nandakumaran ,&nbsp;Sankar Kasinathan","doi":"10.1016/j.nonrwa.2025.104501","DOIUrl":"10.1016/j.nonrwa.2025.104501","url":null,"abstract":"<div><div>This article addresses the homogenization of the heat equation involving the <span><math><mi>p</mi></math></span>-Laplacian in non-cylindrical domains with an evolving oscillating boundary. A change of coordinates is employed to transform the heat equations with <span><math><mi>p</mi></math></span>-Laplacian into parabolic <span><math><mi>p</mi></math></span>-Laplacian equations featuring oscillating coefficients in a reference domain. One novelty of this article is that the equation in the reference domain consists of an oscillating coefficient matrix in the nonlinear component, specifically <span><math><msup><mrow><mo>|</mo><msubsup><mi>M</mi><mrow><mrow><mi>ε</mi></mrow></mrow><mrow><mi>t</mi><mi>r</mi></mrow></msubsup><mi>∇</mi><msub><mi>U</mi><mrow><mi>ε</mi></mrow></msub><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup></math></span>. The existence and uniqueness of solutions are demonstrated in the reference domain through a non-trivial Galerkin approximation, accompanied by a significant <span><math><mrow><mi>ε</mi></mrow></math></span>-uniform estimate. On the other hand, a modified two-scale convergence method is employed to derive the two-scale homogenized problem. Furthermore, an explicit solution to the nonlinear cell problem is constructed. This solution is employed to drive the effective equation within the reference domain and corrector result, identified as a transformed effective problem of the heat equation with <span><math><mi>p</mi></math></span>-Laplacian in a non-cylindrical domain featuring an effective evolving boundary.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104501"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099835","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":"Global solutions to the angiogenesis system with p-Laplacian diffusion","authors":"Changchun Liu,&nbsp;Yue Zhou","doi":"10.1016/j.nonrwa.2025.104478","DOIUrl":"10.1016/j.nonrwa.2025.104478","url":null,"abstract":"<div><div>In this paper, we consider a angiogenesis system with <span><math><mi>p</mi></math></span>-Laplacian diffusion <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>∇</mo><mi>⋅</mi><mfenced><mrow><mrow><mo>(</mo><msup><mrow><mfenced><mrow><mo>∇</mo><mi>u</mi></mrow></mfenced></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>+</mo><mi>δ</mi><mo>)</mo></mrow><mo>∇</mo><mi>u</mi></mrow></mfenced><mo>−</mo><mi>χ</mi><mo>∇</mo><mi>⋅</mi><mfenced><mrow><mi>u</mi><mo>∇</mo><mi>v</mi></mrow></mfenced><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace></mtd><mtd><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>−</mo><mi>u</mi><mi>v</mi><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace></mtd><mtd><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>in a bounded domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mrow><mo>(</mo><mi>N</mi><mo>≥</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> with smooth boundary. For all <span><span><span><math><mrow><mi>p</mi><mo>&gt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mo>∗</mo></mrow></msub><mo>=</mo><mo>max</mo><mrow><mo>{</mo><mn>2</mn><mo>,</mo><mfrac><mrow><mn>1</mn><mo>+</mo><msqrt><mrow><mn>1</mn><mo>+</mo><mn>4</mn><mi>N</mi></mrow></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>}</mo></mrow><mo>,</mo></mrow></math></span></span></span>we prove the existence of global strong solution.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104478"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144858431","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":"Partial regularity and the upper Minkowski dimension of singularities for suitable weak solutions to the 3D co-rotational Beris-Edwards system","authors":"Qiao Liu,&nbsp;Zhongbao Zuo","doi":"10.1016/j.nonrwa.2025.104511","DOIUrl":"10.1016/j.nonrwa.2025.104511","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We study partial regularity and the upper Minkowski dimension of potential singularities for suitable weak solutions to the 3d co-rotational Beris-Edwards system for the nematic liquid crystal flows with Landau-de Gennes potential. Precisely, we establish that there exists a &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; such that if &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is a suitable weak solution, and satisfies&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msubsup&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;/msubsup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;∥&lt;/mo&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;/mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∥&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/msubsup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;∥&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;∥&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/msubsup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mfrac&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, then &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is regular at &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. Based upon the regularity result above, we then prove the upper Minkowski dimension of the potential singularities for any suitable weak solution is at most &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mn&gt;975&lt;/mn&gt;&lt;mn&gt;758&lt;/mn&gt;&lt;/mfrac&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;≈&lt;/mo&gt;&lt;mn&gt;1.286&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Additionally, if &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104511"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157518","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":"Limit cycles of a class of hybrid piecewise differential systems with a discontinuity line of L shape","authors":"Marly Tatiana Anacona Cabrera ,&nbsp;Gerardo Anacona Erazo ,&nbsp;Jaume Llibre","doi":"10.1016/j.nonrwa.2025.104492","DOIUrl":"10.1016/j.nonrwa.2025.104492","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this work we study a class of discontinuous hybrid piecewise differential systems formed by two Hamiltonian systems that we named piecewise hybrid Hamiltonian systems. More precisely, we consider the differential systems with Hamiltonian functions &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&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;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;x&lt;/mi&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;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;y&lt;/mi&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;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&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;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&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;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mtext&gt;if&lt;/mtext&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;Σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mtext&gt;if&lt;/mtext&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;Σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;with reset maps &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; on &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; on &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; for &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; are either zero, or one of them is a nonzero homogeneous polynomial of degree 3, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;Σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&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","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104492"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157517","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 a fractional boundary version of Talenti’s inequality in the unit ball","authors":"Yassin El Karrouchi,&nbsp;Tobias Weth","doi":"10.1016/j.nonrwa.2025.104482","DOIUrl":"10.1016/j.nonrwa.2025.104482","url":null,"abstract":"<div><div>Inspired by recent work of Ferone and Volzone (2021), we derive sufficient conditions for the validity and non-validity of a boundary version of Talenti’s comparison principle in the context of Dirichlet–Poisson problems for the fractional Laplacian <span><math><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup></math></span> in the unit ball <span><math><mrow><mi>Ω</mi><mo>=</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span>, <span><math><mrow><mi>s</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. In particular, our results imply a universal failure of the classical pointwise Talenti inequality in the fractional radial context. In contrast, a boundary Talenti type inequality holds for radial functions in the higher order case <span><math><mrow><mi>s</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104482"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932349","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":"Symmetry breaking for nonhomogeneous Hénon-type problems involving the 1-Laplacian operator","authors":"Marcos T.O. Pimenta ,&nbsp;Yino B. Cueva Carranza ,&nbsp;Giovany M. Figueiredo ,&nbsp;Olimpio Hiroshi Miyagaki","doi":"10.1016/j.nonrwa.2025.104480","DOIUrl":"10.1016/j.nonrwa.2025.104480","url":null,"abstract":"<div><div>In this paper we study the nonhomogeneous Hénon elliptic problem involving the 1-Laplacian operator within the unit ball. Under some assumptions on the nonlinearity, and for sufficiently large parameter values, we establish the existence of a non-radial solution. Our approach relies on an approximation scheme in which the solution is obtained as the limit of solutions to <span><math><mi>p</mi></math></span>-Laplacian type problems.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104480"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144852257","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 value function for optimal control of semilinear parabolic equations","authors":"Eduardo Casas ,&nbsp;Karl Kunisch ,&nbsp;Fredi Tröltzsch","doi":"10.1016/j.nonrwa.2025.104508","DOIUrl":"10.1016/j.nonrwa.2025.104508","url":null,"abstract":"<div><div>The value function for an infinite horizon tracking type optimal control problem with semilinear parabolic equation is investigated. In view of a possible nonconvexity of the optimal control problem, a local version of the value function is considered. Its differentiability is proved for initial data in a neighborhood around the nominal initial value, provided a second order sufficient optimality condition is fulfilled for the nominal locally optimal control. Based on the differentiability of the value function, a Hamilton-Jacobi-Bellman equation is derived.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104508"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157632","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}