Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"Existence results for a borderline case of a class of p-Laplacian problems","authors":"Anna Maria Candela , Kanishka Perera , Addolorata Salvatore","doi":"10.1016/j.na.2025.113762","DOIUrl":"10.1016/j.na.2025.113762","url":null,"abstract":"<div><div>The aim of this paper is investigating the existence of at least one nontrivial bounded solution of the new asymptotically “linear” problem <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mo>div</mo><mfenced><mrow><mfenced><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><mi>A</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msup></mrow></mfenced><msup><mrow><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>∇</mo><mi>u</mi></mrow></mfenced><mo>+</mo><mi>s</mi><mspace></mspace><mi>A</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mi>s</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mspace></mspace><msup><mrow><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi></mrow></msup></mtd></mtr><mtr><mtd><mspace></mspace><mspace></mspace><mspace></mspace><mo>=</mo><mspace></mspace><mi>μ</mi><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mrow><mo>(</mo><mi>s</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow></mtd><mtd><mtext>in</mtext><mi>Ω</mi><mtext>,</mtext></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn></mtd><mtd><mtext>on</mtext><mi>∂</mi><mi>Ω</mi><mtext>,</mtext></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mi>Ω</mi></math></span> is a bounded domain in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>, <span><math><mrow><mi>N</mi><mo>≥</mo><mn>2</mn></mrow></math></span>, <span><math><mrow><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mi>N</mi></mrow></math></span>, <span><math><mrow><mi>s</mi><mo>></mo><mn>1</mn><mo>/</mo><mi>p</mi></mrow></math></span>, both the coefficients <span><math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>A</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> are in <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> and far away from 0, <span><math><mrow><mi>μ</mi><mo>∈</mo><mi>R</mi></mrow></math></span>, and the “perturbation” term <span><math><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> is a Carathéodory function on <span><math><mrow><mi>Ω</mi><mo>×</mo><mi>R</mi></mrow></math></span> which grows as <span><math><msup><mrow><mrow><mo>|</mo><mi>t</mi><mo>|</mo></mrow></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span> with <span><math><mrow><mn>1</m","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113762"},"PeriodicalIF":1.3,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143265967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Variational integrals on Hessian spaces: Partial regularity for critical points","authors":"Arunima Bhattacharya ,&nbsp;Anna Skorobogatova","doi":"10.1016/j.na.2025.113760","DOIUrl":"10.1016/j.na.2025.113760","url":null,"abstract":"<div><div>We develop regularity theory for critical points of variational integrals defined on Hessian spaces of functions on open, bounded subdomains of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, under compactly supported variations. We show that for smooth convex functionals, a <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>∞</mi></mrow></msup></math></span> critical point with bounded Hessian is smooth provided that its Hessian has a small bounded mean oscillation (BMO). We deduce that the interior singular set of a critical point has Hausdorff dimension at most <span><math><mrow><mi>n</mi><mo>−</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span>, for some <span><math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span>. We state some applications of our results to variational problems in Lagrangian geometry. Finally, we use the Hamiltonian stationary equation to demonstrate the importance of our assumption on the a priori regularity of the critical point.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113760"},"PeriodicalIF":1.3,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143268147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Corrigendum to “Hörmander type theorems for multi-linear and multi-parameter Fourier multiplier operators with limited smoothness” [Nonlinear Anal. 101 (2014) 98–112]","authors":"Jiao Chen ,&nbsp;Guozhen Lu","doi":"10.1016/j.na.2025.113750","DOIUrl":"10.1016/j.na.2025.113750","url":null,"abstract":"","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113750"},"PeriodicalIF":1.3,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local uniqueness of minimizers for Choquard type equations","authors":"Lintao Liu ,&nbsp;Kaimin Teng ,&nbsp;Shuai Yuan","doi":"10.1016/j.na.2025.113764","DOIUrl":"10.1016/j.na.2025.113764","url":null,"abstract":"<div><div>We consider <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-constraint minimizers of the Choquard energy functional with a trapping potential <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>. It is known that positive minimizers exist if and only if the parameter <span><math><mi>a</mi></math></span> satisfies <span><math><mrow><mi>a</mi><mo>&lt;</mo><msup><mrow><mi>a</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>≔</mo><msubsup><mrow><mo>‖</mo><mi>Q</mi><mo>‖</mo></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></math></span>, where <span><math><mi>Q</mi></math></span> is the unique positive radial solution of <span><math><mrow><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>u</mi><mo>−</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup><mi>u</mi><mo>=</mo><mn>0</mn></mrow></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. This paper focuses on the local uniqueness of minimizers by using energy estimates, blow-up analysis and establishing the Pohozăev identity.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113764"},"PeriodicalIF":1.3,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fujita exponent and blow-up rate for a mixed local and nonlocal heat equation","authors":"Leandro M. Del Pezzo ,&nbsp;Raúl Ferreira","doi":"10.1016/j.na.2025.113761","DOIUrl":"10.1016/j.na.2025.113761","url":null,"abstract":"<div><div>In this paper we consider the blow-up problem for a mixed local-nonlocal diffusion operator, <span><span><span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>a</mi><mi>Δ</mi><mi>u</mi><mo>−</mo><mi>b</mi><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>+</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msup></mrow></math></span></span></span>We show that the Fujita exponent is given by the nonlocal part, <span><math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>F</mi></mrow></msub><mo>=</mo><mn>1</mn><mo>+</mo><mn>2</mn><mi>s</mi><mo>/</mo><mi>N</mi></mrow></math></span>. We also determinate, in some cases, the blow-up rate.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113761"},"PeriodicalIF":1.3,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Extremal functions for twisted sharp Sobolev inequalities with lower order remainder terms","authors":"Olivier Druet ,&nbsp;Emmanuel Hebey","doi":"10.1016/j.na.2025.113758","DOIUrl":"10.1016/j.na.2025.113758","url":null,"abstract":"<div><div>We prove existence of extremal functions and compactness of the set of extremal functions for twisted sharp 4-dimensional Sobolev inequalities with lower order remainder terms.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113758"},"PeriodicalIF":1.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Universal differentiability sets in Laakso space","authors":"Sylvester Eriksson-Bique ,&nbsp;Andrea Pinamonti ,&nbsp;Gareth Speight","doi":"10.1016/j.na.2025.113752","DOIUrl":"10.1016/j.na.2025.113752","url":null,"abstract":"<div><div>We show that there exists a family of mutually singular doubling measures on Laakso space with respect to which real-valued Lipschitz functions are almost everywhere differentiable. This implies that there exists a measure zero universal differentiability set in Laakso space. Additionally, we show that each of the measures constructed supports a Poincaré inequality.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113752"},"PeriodicalIF":1.3,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Semiclassical states for the curl–curl problem","authors":"Bartosz Bieganowski ,&nbsp;Adam Konysz ,&nbsp;Jarosław Mederski","doi":"10.1016/j.na.2025.113756","DOIUrl":"10.1016/j.na.2025.113756","url":null,"abstract":"<div><div>We show the existence of the so-called semiclassical states <span><math><mrow><mi>U</mi><mo>:</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span> to the following curl–curl problem <span><math><mrow><msup><mrow><mi>ɛ</mi></mrow><mrow><mn>2</mn></mrow></msup><mspace></mspace><mo>∇</mo><mo>×</mo><mrow><mo>(</mo><mo>∇</mo><mo>×</mo><mi>U</mi><mo>)</mo></mrow><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>U</mi><mo>=</mo><mi>g</mi><mrow><mo>(</mo><mi>U</mi><mo>)</mo></mrow><mo>,</mo></mrow></math></span> for sufficiently small <span><math><mrow><mi>ɛ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. We study the asymptotic behaviour of solutions as <span><math><mrow><mi>ɛ</mi><mo>→</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow></math></span> and we investigate also a related nonlinear Schrödinger equation involving a singular potential. The problem models large permeability nonlinear materials satisfying the system of Maxwell equations.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113756"},"PeriodicalIF":1.3,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Radial positive solutions for mixed local and nonlocal supercritical Neumann problem","authors":"David Amundsen,&nbsp;Abbas Moameni,&nbsp;Remi Yvant Temgoua","doi":"10.1016/j.na.2025.113763","DOIUrl":"10.1016/j.na.2025.113763","url":null,"abstract":"<div><div>In this paper, we establish the existence of positive non-decreasing radial solutions for a nonlinear mixed local and nonlocal Neumann problem in the ball. No growth assumption on the nonlinearity is required. We also provide a criterion for the existence of non-constant solutions provided the problem possesses a trivial constant solution.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113763"},"PeriodicalIF":1.3,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gradient Einstein-type warped products: Rigidity, existence and nonexistence results via a nonlinear PDE","authors":"José Nazareno Vieira Gomes ,&nbsp;Willian Isao Tokura","doi":"10.1016/j.na.2025.113759","DOIUrl":"10.1016/j.na.2025.113759","url":null,"abstract":"<div><div>We establish the necessary and sufficient conditions for constructing gradient Einstein-type warped metrics. One of these conditions leads us to a general Lichnerowicz equation with analytic and geometric coefficients for this class of metrics on the space of warping functions. In this way, we prove gradient estimates for positive solutions of a nonlinear elliptic differential equation on a complete Riemannian manifold with associated Bakry–Émery Ricci tensor bounded from below. As an application, we provide nonexistence and rigidity results for a large class of gradient Einstein-type warped metrics. Furthermore, we show how to construct gradient Einstein-type warped metrics, and then we give explicit examples which are not only meaningful in their own right, but also help to justify our results.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"255 ","pages":"Article 113759"},"PeriodicalIF":1.3,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}