Journal of Mathematical Analysis and Applications最新文献

{"title":"Weak-strong uniqueness for a specific class of cross-diffusion models with volume filling","authors":"Ling Liu","doi":"10.1016/j.jmaa.2025.129727","DOIUrl":"10.1016/j.jmaa.2025.129727","url":null,"abstract":"<div><div>The weak-strong uniqueness for solutions to a special class of parabolic cross-diffusion systems with volume filling in a bounded domain with no-flux boundary conditions is proved. The diffusion matrix is neither symmetric nor positive definite, but the system possesses a formal gradient-flow or entropy structure. It is shown that any weak solution coincides with a “strong” solution with the same initial data, as long as the “strong” solution exists. The proof is mainly based on the use of the relative entropy modified by small parameters <em>ε</em> and <em>δ</em>, combined with some analytical techniques.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129727"},"PeriodicalIF":1.2,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170500","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":"Finite-time stabilization of a class of unbounded parabolic bilinear systems in Hilbert space","authors":"Younes Amaliki,&nbsp;Mohamed Ouzahra","doi":"10.1016/j.jmaa.2025.129720","DOIUrl":"10.1016/j.jmaa.2025.129720","url":null,"abstract":"<div><div>This paper investigates the finite-time stabilization of a class of unbounded bilinear systems in Hilbert spaces. Our methodology involves decomposing the original system into two interconnected subsystems: one that either inherently possesses finite-time stability or lacks it regardless of the feedback control applied, and another for which an appropriate feedback control must be designed to ensure the desired stability properties. By employing the theory of maximal monotone operators and Lyapunov-based methods, we establish sufficient conditions for finite-time stability without assuming the coercivity of the control operator. Applications are presented for heat and biharmonic heat equations, demonstrating the practical relevance of the results. This work extends existing frameworks and provides a broader theoretical foundation for the study of unbounded bilinear systems.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129720"},"PeriodicalIF":1.2,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147729","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":"Takagi–van der Waerden functions in metric spaces and their Lipschitz derivatives","authors":"Oleksandr V. Maslyuchenko ,&nbsp;Ziemowit M. Wójcicki","doi":"10.1016/j.jmaa.2025.129726","DOIUrl":"10.1016/j.jmaa.2025.129726","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We introduce the Takagi–van der Waerden function with parameters &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; by setting &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&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;munderover&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/munderover&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is a maximal &lt;span&gt;&lt;math&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt;-separated set in a metric space &lt;em&gt;X&lt;/em&gt;. So, if &lt;span&gt;&lt;math&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; then &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is the Takagi function and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is the van der Waerden function which are well-known examples of nowhere differentiable functions. Then we prove that the big Lipschitz derivative &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Lip&lt;/mi&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&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;mo&gt;+&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; if &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and &lt;em&gt;x&lt;/em&gt; is a non-isolated point of &lt;em&gt;X&lt;/em&gt;. Moreover, if the shell porosity &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&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;&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; for some &lt;em&gt;λ&lt;/em&gt; and each non-isolated point &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; then the little Lipschitz derivative &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;lip&lt;/mi&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&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;mo&gt;+&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; for large enough &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and any non-isolated point &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. In particular, this is true for any normed space. Finally, we prove that for any open set &lt;em&gt;A&lt;/em&gt; in a metric (normed) space &lt;em&gt;X&lt;/em&gt; without isolated points there exists a continuous function &lt;em&gt;f&lt;/em&gt; such that &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Lip&lt;/mi&gt;&lt;/mrow&gt;&lt;mi&gt;f&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;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; (and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;lip&lt;/mi&gt;&lt;/mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129726"},"PeriodicalIF":1.2,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170510","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":"Heyde characterization theorem for some classes of locally compact Abelian groups","authors":"Gennadiy Feldman","doi":"10.1016/j.jmaa.2025.129717","DOIUrl":"10.1016/j.jmaa.2025.129717","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> be linear forms of real-valued independent random variables. By Heyde's theorem, if the conditional distribution of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> given <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is symmetric, then the random variables are Gaussian. A number of papers are devoted to generalization of Heyde's theorem to the case, where independent random variables take values in a locally compact Abelian group <em>X</em>. The article continues these studies. We consider the case, where <em>X</em> is either a totally disconnected group or is of the form <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><mi>G</mi></math></span>, where <em>G</em> is a totally disconnected group consisting of compact elements. The proof is based on the study of solutions of the Heyde functional equation on the character group of the original group. In so doing, we use methods of abstract harmonic analysis.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129717"},"PeriodicalIF":1.2,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170498","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":"Spectral gap estimates for the biharmonic operator on submanifolds of negatively curved spaces","authors":"Hezi Lin","doi":"10.1016/j.jmaa.2025.129704","DOIUrl":"10.1016/j.jmaa.2025.129704","url":null,"abstract":"<div><div>In this paper, we firstly establish two general functional inequalities on bounded domains of Riemannian manifolds carrying a special kind of function. Using this general inequalities and the comparison technique, we thereby obtain lower bound estimates for the first eigenvalues of the biharmonic operators on domains of submanifolds with controlled mean curvature and under various extrinsic curvature conditions. Meanwhile, we give some higher-order estimates concerning these problems.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129704"},"PeriodicalIF":1.2,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138485","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 mappings generating embedding operators in Sobolev classes on metric measure spaces","authors":"Alexander Menovschikov ,&nbsp;Alexander Ukhlov","doi":"10.1016/j.jmaa.2025.129716","DOIUrl":"10.1016/j.jmaa.2025.129716","url":null,"abstract":"<div><div>In this article, we study homeomorphisms <span><math><mi>φ</mi><mo>:</mo><mi>Ω</mi><mo>→</mo><mover><mrow><mi>Ω</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span> that generate embedding operators in Sobolev classes on metric measure spaces <em>X</em> by the composition rule <span><math><msup><mrow><mi>φ</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>f</mi><mo>)</mo><mo>=</mo><mi>f</mi><mo>∘</mo><mi>φ</mi></math></span>. In turn, this leads to Sobolev type embedding theorems for a wide class of domains <span><math><mover><mrow><mi>Ω</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>⊂</mo><mi>X</mi></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129716"},"PeriodicalIF":1.2,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170499","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 semipositone problems over RN for the fractional p-Laplace operator","authors":"Nirjan Biswas ,&nbsp;Rohit Kumar","doi":"10.1016/j.jmaa.2025.129703","DOIUrl":"10.1016/j.jmaa.2025.129703","url":null,"abstract":"&lt;div&gt;&lt;div&gt;For &lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; we find a positive solution to the following class of semipositone problems associated with the fractional &lt;em&gt;p&lt;/em&gt;-Laplace operator:&lt;span&gt;&lt;span&gt;&lt;span&gt;(SP)&lt;/span&gt;&lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mtext&gt; in &lt;/mtext&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&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;g&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&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;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∩&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&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;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is a positive function, &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; is a parameter and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is defined as &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; for &lt;span&gt;&lt;math&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; for &lt;span&gt;&lt;math&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; for &lt;span&gt;&lt;math&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;em&gt;f&lt;/em&gt; is a non-negative continuous function on &lt;span&gt;&lt;math&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; satisfies &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; with subcritical and Ambrosetti-Rabinowitz type growth. Depending on the range of &lt;em&gt;a&lt;/em&gt;, we obtain the existence of a mountain pass solution to (SP) in &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&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;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Then, we prove mountain pass solutions are uniformly bounded with respect to &lt;em&gt;a&lt;/em&gt;, over &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mr","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129703"},"PeriodicalIF":1.2,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170767","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":"Upper bounds of the lifespan estimates for semilinear wave equations with damping and potential in high dimensional Schwarzschild spacetime","authors":"Mengliang Liu ,&nbsp;Mengyun Liu","doi":"10.1016/j.jmaa.2025.129702","DOIUrl":"10.1016/j.jmaa.2025.129702","url":null,"abstract":"<div><div>In this work, we study finite time blow-up phenomena for power-type semilinear wave equations in high-dimensional Schwarzschild spacetime with damping and potential terms. By carefully constructing test functions in the weak formulation of the solution, we establish blow-up results and derive sharp upper bounds for lifespan estimates.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129702"},"PeriodicalIF":1.2,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134932","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":"Convergence of linear solutions through convergence of periodic initial data","authors":"Harrison Gaebler ,&nbsp;Wesley R. Perkins","doi":"10.1016/j.jmaa.2025.129698","DOIUrl":"10.1016/j.jmaa.2025.129698","url":null,"abstract":"<div><div>When studying the stability of <em>T</em>-periodic solutions to partial differential equations, it is common to encounter subharmonic perturbations, i.e. perturbations which have a period that is an integer multiple (say <em>n</em>) of the background wave, and localized perturbations, i.e. perturbations that are integrable on the line. Formally, we expect solutions subjected to subharmonic perturbations to converge to solutions subjected to localized perturbations as <em>n</em> tends to infinity since larger <em>n</em> values force the subharmonic perturbation to become more localized. In this paper, we study the convergence of solutions to linear initial value problems when subjected to subharmonic and localized perturbations. In particular, we prove the formal intuition outlined above; namely, we prove that if the subharmonic initial data converges to some localized initial datum, then the linear solutions converge.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 1","pages":"Article 129698"},"PeriodicalIF":1.2,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170350","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":"Trace theory for gauge-covariant Sobolev spaces","authors":"Jean Van Schaftingen,&nbsp;Leon Winter","doi":"10.1016/j.jmaa.2025.129697","DOIUrl":"10.1016/j.jmaa.2025.129697","url":null,"abstract":"<div><div>The traces of gauge-covariant Sobolev spaces on a Riemannian vector bundle endowed with a metric connection are characterised as some gauge-covariant fractional Sobolev spaces when the curvature of the connection is bounded. The constants in the trace and extension theorems only depend on this curvature. When the connection is abelian, one recovers known results for magnetic Sobolev spaces.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129697"},"PeriodicalIF":1.2,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169162","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}