Journal of Mathematical Analysis and Applications最新文献

{"title":"Normalized solutions for the mass supercritical Kirchhoff problem","authors":"Liu Gao,&nbsp;Zhong Tan","doi":"10.1016/j.jmaa.2025.129475","DOIUrl":"10.1016/j.jmaa.2025.129475","url":null,"abstract":"<div><div>In the present paper, we are concerned with the existence of normalized solutions for the Kirchhoff problem, where the nonlinear term exhibits some new weak mass supercritical conditions. By employing analytical techniques and critical point theorems, we establish several new existence results. Our main results improve and complement the works of He et al. <span><span>[10]</span></span>, Wang and Qian (2023) <span><span>[22]</span></span> and some other related literature.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129475"},"PeriodicalIF":1.2,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636628","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":"Analysis of SIS infectious disease dynamics with linear external sources and free boundaries: A computational and theoretical perspective","authors":"Yarong Zhang ,&nbsp;Meng Hu ,&nbsp;Jie Zheng ,&nbsp;Xinyu Shi","doi":"10.1016/j.jmaa.2025.129448","DOIUrl":"10.1016/j.jmaa.2025.129448","url":null,"abstract":"<div><div>The spatio-temporal distribution of individuals within the SIS (Susceptible-Infected-Susceptible) model is pivotal for the effective prevention and control of infectious diseases. This study leverages the reaction-diffusion epidemic model to improve the accuracy of identifying infected areas and predicting potential outbreaks. Compression mapping and the standard theory of parabolic equations are applied to analyze the dynamics of susceptible individuals influenced by linear external sources, simulating their birth and death rates. Key findings reveal a dichotomous relationship between the spread and extinction of infectious diseases, dictated by the time-dependent basic reproduction number. Furthermore, the study investigates the impact of the diffusion coefficient, the propagation potential of infected individuals, and the initial infection range on disease dissemination or attenuation. Numerical simulations support the theoretical findings, indicating that a high expanding capacity of infected individuals poses challenges to effective disease prevention and control. This work provides novel insights into the spatio-temporal dynamics of the SIS model and lays a foundation for future research endeavours in this domain.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129448"},"PeriodicalIF":1.2,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621372","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 and global properties of spaces of minimal usco maps","authors":"Serhii Bardyla ,&nbsp;Branislav Novotný ,&nbsp;Jaroslav Šupina","doi":"10.1016/j.jmaa.2025.129472","DOIUrl":"10.1016/j.jmaa.2025.129472","url":null,"abstract":"<div><div>In this paper, we study an interplay between local and global properties of spaces of minimal usco maps equipped with the topology of uniform convergence on compact sets. In particular, for each locally compact space <em>X</em> and metric space <em>Y</em>, we characterize the space of minimal usco maps from <em>X</em> to <em>Y</em>, satisfying one of the following properties: (i) compact, (ii) locally compact, (iii) <em>σ</em>-compact, (iv) locally <em>σ</em>-compact, (v) metrizable, (vi) ccc, (vii) locally ccc, where in the last two items we additionally assumed that <em>Y</em> is separable and non-discrete. Some of the aforementioned results complement ones of Ľubica Holá and Dušan Holý. Also, we obtain analogous characterizations for spaces of minimal cusco maps.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129472"},"PeriodicalIF":1.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143637087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Boundedness and global existence in a higher-dimensional parabolic-elliptic-ODE chemotaxis-haptotaxis model with remodeling of non-diffusible attractant","authors":"Ling Liu","doi":"10.1016/j.jmaa.2025.129473","DOIUrl":"10.1016/j.jmaa.2025.129473","url":null,"abstract":"<div><div>This paper addresses the issue of boundedness for solutions to the following quasilinear chemotaxis-haptotaxis model of parabolic-elliptic-ODE type:<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>−</mo><mi>χ</mi><mi>∇</mi><mo>⋅</mo><mo>(</mo><mi>u</mi><mi>∇</mi><mi>v</mi><mo>)</mo><mo>−</mo><mi>ξ</mi><mi>∇</mi><mo>⋅</mo><mo>(</mo><mi>u</mi><mi>∇</mi><mi>w</mi><mo>)</mo><mo>+</mo><mi>u</mi><mo>(</mo><mi>r</mi><mo>−</mo><mi>μ</mi><msup><mrow><mi>u</mi></mrow><mrow><mi>γ</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>−</mo><mi>w</mi><mo>)</mo><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><mn>0</mn><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>+</mo><mi>u</mi><mo>−</mo><mi>v</mi><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>w</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>−</mo><mi>v</mi><mi>w</mi><mo>+</mo><mi>η</mi><mi>w</mi><mo>(</mo><mn>1</mn><mo>−</mo><mi>u</mi><mo>−</mo><mi>w</mi><mo>)</mo><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> subject to zero-flux boundary conditions within a smooth, bounded domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> (with <span><math><mi>N</mi><mo>≥</mo><mn>3</mn></math></span>). The parameters involved are <span><math><mi>χ</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo><mi>μ</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo><mi>r</mi><mo>≥</mo><mn>0</mn></math></span>, and <span><math><mi>η</mi><mo>&gt;</mo><mn>0</mn></math></span>. It is demonstrated that, provided <span><math><mi>γ</mi><mo>&gt;</mo><mn>3</mn><mo>−</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mi>N</mi></mrow></mfrac></math></span>, for sufficiently smooth initial data, the corresponding initial-boundary problem admits a unique global-in-time classical solution, which remains uniformly bounded. To the best of our knowledge, these are the first results concerning the boundedness of solutions for this parabolic-elliptic-ODE system in higher dimensions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129473"},"PeriodicalIF":1.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600799","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":"Large time behavior of a quasilinear two-species attraction-repulsion chemotaxis system with two chemicals","authors":"Miaoqing Tian ,&nbsp;Fuxin Yu ,&nbsp;Xinchun Gao ,&nbsp;Jiahui Hu","doi":"10.1016/j.jmaa.2025.129471","DOIUrl":"10.1016/j.jmaa.2025.129471","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This paper deals with the quasilinear two-species attraction-repulsion chemotaxis system with two chemicals: &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&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;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&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;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&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;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&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;/msup&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&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;mi&gt;w&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&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;/msup&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, subject to the homogeneous Neumann boundary conditions in a bounded domain &lt;span&gt;&lt;math&gt;&lt;mi&gt;Ω&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;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;(&lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;) with smooth boundary, where the parameters &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&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;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&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;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&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;msub&gt;&lt;mrow&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&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","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129471"},"PeriodicalIF":1.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636616","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":"Normalized solutions of a (2,p)-Laplacian equation","authors":"Xiaoli Zhu,&nbsp;Yunli Zhao,&nbsp;Zhanping Liang","doi":"10.1016/j.jmaa.2025.129462","DOIUrl":"10.1016/j.jmaa.2025.129462","url":null,"abstract":"<div><div>In this paper, we are concerned with normalized solutions of a <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mi>p</mi><mo>)</mo></math></span>-Laplacian equation with an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> constraint in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, where <span><math><mn>2</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mn>3</mn></math></span>. Different from literature previous, we focus on the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> not <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> constraint for <span><math><mi>p</mi><mo>&gt;</mo><mn>2</mn></math></span>. Moreover, an interesting finding is that the non-homogeneity driven by the operators Δ and <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> has an important impact on <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> constraint <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mi>p</mi><mo>)</mo></math></span>-Laplacian equations, as reflected in the definition of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> critical exponent, and the existence of normalized solutions in both <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> subcritical and supercritical cases. All these new phenomena, which are different from those exhibited by a single <em>p</em>-Laplacian equation, reveal the essential characteristics of <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mi>p</mi><mo>)</mo></math></span>-Laplacian equations.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129462"},"PeriodicalIF":1.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636614","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":"Asymptotic expansions for the generalised trigonometric integral and its zeros","authors":"Gergő Nemes","doi":"10.1016/j.jmaa.2025.129463","DOIUrl":"10.1016/j.jmaa.2025.129463","url":null,"abstract":"<div><div>In this paper, we investigate the asymptotic properties of the generalised trigonometric integral <span><math><mi>ti</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>α</mi><mo>)</mo></math></span> and its associated modulus and phase functions for large complex values of <em>z</em>. We derive asymptotic expansions for these functions, accompanied by explicit and computable error bounds. For real values of <em>a</em>, the function <span><math><mi>ti</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>α</mi><mo>)</mo></math></span> possesses infinitely many positive real zeros. Assuming <span><math><mi>a</mi><mo>&lt;</mo><mn>1</mn></math></span>, we establish asymptotic expansions for the large zeros, accompanied by precise error estimates. The error bounds for the asymptotics of the phase function and its zeros will be derived by studying the analytic properties of both the phase function and its inverse. Additionally, we demonstrate that for real variables, the derived asymptotic expansions are enveloping, meaning that successive partial sums provide upper and lower bounds for the corresponding functions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129463"},"PeriodicalIF":1.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600801","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":"Semiclassical limit of a non-polynomial q-Askey scheme","authors":"Jonatan Lenells ,&nbsp;Julien Roussillon","doi":"10.1016/j.jmaa.2025.129474","DOIUrl":"10.1016/j.jmaa.2025.129474","url":null,"abstract":"<div><div>We prove a semiclassical asymptotic formula for the two elements <span><math><mi>M</mi></math></span> and <span><math><mi>Q</mi></math></span> lying at the bottom of the recently constructed non-polynomial hyperbolic <em>q</em>-Askey scheme. We also prove that the corresponding exponent is a generating function of the canonical transformation between pairs of Darboux coordinates on the monodromy manifold of the Painlevé I and <span><math><msub><mrow><mtext>III</mtext></mrow><mrow><mn>3</mn></mrow></msub></math></span> equations, respectively. Such pairs of coordinates characterize the asymptotics of the tau function of the corresponding Painlevé equation. We conjecture that the other members of the non-polynomial hyperbolic <em>q</em>-Askey scheme yield generating functions associated to the other Painlevé equations in the semiclassical limit.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129474"},"PeriodicalIF":1.2,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics and optimal control of an SIVR immuno-epidemiological model with standard incidence","authors":"Xi-Chao Duan ,&nbsp;Chenyu Zhu ,&nbsp;Xue-Zhi Li ,&nbsp;Eric Numfor ,&nbsp;Maia Martcheva","doi":"10.1016/j.jmaa.2025.129449","DOIUrl":"10.1016/j.jmaa.2025.129449","url":null,"abstract":"<div><div>Based on the immuno-epidemiological model concept, we propose a susceptible–infected–vaccinated–recovered epidemic model with between-host transmission and within-host infection, where disease transmission between hosts is described by a standard incidence rate and the within-host infection process is governed by a bilinear incidence rate. The basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>ψ</mi><mo>)</mo></math></span> in the between-host model strongly depends on the within-host infection process. If <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>ψ</mi><mo>)</mo><mo>&lt;</mo><mn>1</mn></math></span>, the disease-free steady state <span><math><msup><mrow><mi>E</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> of the between-host epidemic model is locally stable, and if <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>ψ</mi><mo>)</mo><mo>&gt;</mo><mn>1</mn></math></span>, the endemic steady state <span><math><msup><mrow><mi>E</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> of the between-host epidemic model is locally stable. If <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo><mo>&lt;</mo><mn>1</mn></math></span>, the disease-free steady state <span><math><msup><mrow><mi>E</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> of the between-host epidemic model is globally stable. Furthermore, to better understand the roles of within-host treatment and between-host control in disease transmission, we formulated and studied an optimal control problem for the immuno-epidemiological model involving treatment and vaccination. Numerical simulations were conducted to demonstrate the effectiveness of the control strategies in various infection processes. The results showed that the duration of within-host treatment must be longer than the duration of vaccination to better control the spread of the disease.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129449"},"PeriodicalIF":1.2,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636627","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 at infinity for solutions of nonhomogeneous degenerate and singular elliptic equations in exterior domains","authors":"Leonardo P. Bonorino ,&nbsp;Lucas P. Dutra ,&nbsp;Filipe J. dos Santos","doi":"10.1016/j.jmaa.2025.129476","DOIUrl":"10.1016/j.jmaa.2025.129476","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this work, we investigate the existence of the limit at infinity of weak solutions of the nonhomogeneous equation &lt;span&gt;&lt;math&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;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&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;mspace&gt;&lt;/mspace&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;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; in the exterior domain &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;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;﹨&lt;/mo&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;mi&gt;K&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;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; is a compact set. Indeed, for any &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;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;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, we prove that the solutions converge at infinity if &lt;em&gt;A&lt;/em&gt; satisfies some growth conditions and &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&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;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; has some decay property. Moreover, for &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; we can show that the solutions converge at some rate and, for &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, the convergence holds even for some unbounded &lt;em&gt;f&lt;/em&gt;. In addition, for &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, we show that for any continuous function &lt;em&gt;ϕ&lt;/em&gt; defined on ∂&lt;em&gt;K&lt;/em&gt;, the problem&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&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;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&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;mspace&gt;&lt;/mspace&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;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mtext&gt; in &lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&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;mi&gt;K&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mtext&gt; on &lt;/mtext&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; has a bounded weak solution in &lt;span&gt;&lt;math&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mover&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;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;﹨&lt;/mo&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∩&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;C&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;mi&gt;K&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, provided &lt;em&gt;A&lt;/em&gt; and &lt;em&gt;f&lt;/em&gt; are suitable. Furthermore, if &lt;span&gt;&lt;math&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129476"},"PeriodicalIF":1.2,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143684950","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}