Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"Global existence for a Leibenson type equation with reaction on Riemannian manifolds","authors":"Giulia Meglioli ,&nbsp;Francescantonio Oliva ,&nbsp;Francesco Petitta","doi":"10.1016/j.na.2025.113967","DOIUrl":"10.1016/j.na.2025.113967","url":null,"abstract":"<div><div>We show a global existence result for a doubly nonlinear porous medium type equation of the form <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><msup><mrow><mi>u</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>+</mo><mspace></mspace><msup><mrow><mi>u</mi></mrow><mrow><mi>q</mi></mrow></msup></mrow></math></span> on a complete and non-compact Riemannian manifold <span><math><mi>M</mi></math></span> of infinite volume. Here, for <span><math><mrow><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mi>N</mi></mrow></math></span>, we assume <span><math><mrow><mi>m</mi><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>≥</mo><mn>1</mn></mrow></math></span>, <span><math><mrow><mi>m</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mi>q</mi><mo>&gt;</mo><mi>m</mi><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. In particular, under the assumptions that <span><math><mi>M</mi></math></span> supports the Sobolev inequality, we prove that a solution for such a problem exists globally in time provided <span><math><mrow><mi>q</mi><mo>&gt;</mo><mi>m</mi><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mfrac><mrow><mi>p</mi></mrow><mrow><mi>N</mi></mrow></mfrac></mrow></math></span> and the initial datum is small enough; namely, we establish an explicit bound on the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span> norm of the solution at all positive times, in terms of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm of the data. Under the additional assumption that a Poincaré-type inequality also holds in <span><math><mi>M</mi></math></span>, we can establish the same result in the larger interval, i.e. <span><math><mrow><mi>q</mi><mo>&gt;</mo><mi>m</mi><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. This result has no Euclidean counterpart, as it differs entirely from the case of a bounded Euclidean domain due to the fact that <span><math><mi>M</mi></math></span> is non-compact and has infinite measure.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113967"},"PeriodicalIF":1.3,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222823","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":"Improvement of the parabolic regularization method and applications to dispersive models","authors":"Alysson Cunha","doi":"10.1016/j.na.2025.113964","DOIUrl":"10.1016/j.na.2025.113964","url":null,"abstract":"<div><div>We prove that the Benjamin–Ono equation is globally well-posed in <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> for <span><math><mrow><mi>s</mi><mo>&gt;</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>. Our approach does not rely on the global gauge transformation introduced by Tao (Tao, 2004). Instead, we employ a modified version of the standard parabolic regularization method. In particular, this technique also enables us to establish global well-posedness, in the same Sobolev space, for the dispersion-generalized Benjamin–Ono (DGBO) equation.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113964"},"PeriodicalIF":1.3,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223263","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":"Uniform regularity estimates for nonlinear diffusion–advection equations in the hard-congestion limit","authors":"Noemi David ,&nbsp;Filippo Santambrogio ,&nbsp;Markus Schmidtchen","doi":"10.1016/j.na.2025.113953","DOIUrl":"10.1016/j.na.2025.113953","url":null,"abstract":"<div><div>We present regularity results for nonlinear drift–diffusion equations of porous medium type (together with their incompressible limit). We relax the assumptions imposed on the drift term with respect to previous results and additionally study the effect of linear diffusion on our regularity result (a scenario of particular interest in the incompressible case, for it represents the motion of particles driven by a Brownian motion subject to a density constraint). Specifically, this work concerns the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span>-summability of the pressure gradient in porous medium flows with drifts that is stable with respect to the exponent of the nonlinearity, and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-estimates on the pressure Hessian (in particular, in the incompressible case with linear diffusion we prove that the pressure is the positive part of an <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-function).</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113953"},"PeriodicalIF":1.3,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223262","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":"Global and singular solution to a nonlocal model of three-dimensional incompressible Navier–Stokes equations","authors":"Shu Wang,&nbsp;Rulv Li","doi":"10.1016/j.na.2025.113966","DOIUrl":"10.1016/j.na.2025.113966","url":null,"abstract":"<div><div>We in this paper study the singularity formation and global well-posedness of a nonlocal model for some initial boundary condition with a real parameter, which is a one dimensional weak advection model for the three dimensional incompressible Navier–Stokes equations. Based on the Lyapunov functional and contradiction argument, we can prove that the inviscid nonlocal model develops a finite time blowup solution with some even initial data. But, for some special positive parameter and initial data with the given symbol, the inviscid model also has a global smooth solution by the characteristic’ method. Furthermore, by the energy estimations and Gagliardo–Nirenberg inequality, we also obtain that the viscous nonlocal model has a unique global solution with some initial data with the given symbol for all nonnegative parameter. More specially, there is a particular model to the nonlocal model such that the global solution to this model exists for some negative parameter.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113966"},"PeriodicalIF":1.3,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223264","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":"Geodesic loops and orthogonal geodesic chords without self-intersections","authors":"Hans-Bert Rademacher","doi":"10.1016/j.na.2025.113952","DOIUrl":"10.1016/j.na.2025.113952","url":null,"abstract":"<div><div>We show that for a generic Riemannian metric on a compact manifold of dimension <span><math><mrow><mi>n</mi><mo>≥</mo><mn>3</mn></mrow></math></span> all geodesic loops based at a fixed point have no self-intersections. We also show that for an open and dense subset of the space of Riemannian metrics on an <span><math><mi>n</mi></math></span>-disc with <span><math><mrow><mi>n</mi><mo>≥</mo><mn>3</mn></mrow></math></span> and with a strictly convex boundary there are <span><math><mi>n</mi></math></span> geometrically distinct orthogonal geodesic chords without self-intersections. We use a perturbation result for intersecting geodesic segments of the author Rademacher (2024) and a genericity statement due to Bettiol and Giambò (2010) and existence results for orthogonal geodesic chords by Giambò et al. (2018).</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113952"},"PeriodicalIF":1.3,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160065","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":"A geometrical approach to the sharp Hardy inequality in Sobolev–Slobodeckiĭ spaces","authors":"Francesca Bianchi ,&nbsp;Giorgio Stefani ,&nbsp;Anna Chiara Zagati","doi":"10.1016/j.na.2025.113948","DOIUrl":"10.1016/j.na.2025.113948","url":null,"abstract":"<div><div>We give a partial negative answer to a question left open in a previous work by Brasco and the first and third-named authors concerning the sharp constant in the fractional Hardy inequality on convex sets. Our approach has a geometrical flavor and equivalently reformulates the sharp constant in the limit case <span><math><mrow><mi>p</mi><mo>=</mo><mn>1</mn></mrow></math></span> as the Cheeger constant for the fractional perimeter and the Lebesgue measure with a suitable weight. As a by-product, we obtain new lower bounds on the sharp constant in the 1-dimensional case, even for non-convex sets, some of which optimal in the case <span><math><mrow><mi>p</mi><mo>=</mo><mn>1</mn></mrow></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113948"},"PeriodicalIF":1.3,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145134829","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":"Existence of multiple solutions for the generalized abelian Chern–Simons–Higgs model on a torus","authors":"Jongmin Han,&nbsp;Kyungwoo Song","doi":"10.1016/j.na.2025.113950","DOIUrl":"10.1016/j.na.2025.113950","url":null,"abstract":"<div><div>We construct multiple solutions of the generalized self-dual abelian Chern–Simons–Higgs equation in a two-dimensional flat torus by the topological degree method.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113950"},"PeriodicalIF":1.3,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145134830","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":"Behavior of absorbing and generating p-Robin eigenvalues in bounded and exterior domains","authors":"Lukas Bundrock,&nbsp;Tiziana Giorgi,&nbsp;Robert Smits","doi":"10.1016/j.na.2025.113943","DOIUrl":"10.1016/j.na.2025.113943","url":null,"abstract":"<div><div>We establish rigorous quantitative inequalities for the first eigenvalue of the generalized <span><math><mi>p</mi></math></span>-Robin problem, for both the classical diffusion absorption case, where the Robin boundary parameter <span><math><mi>α</mi></math></span> is positive, and the superconducting generation regime (<span><math><mrow><mi>α</mi><mo>&lt;</mo><mn>0</mn></mrow></math></span>), where the boundary acts as a source. In bounded domains, we use a unified approach to derive a precise asymptotic behavior for all <span><math><mi>p</mi></math></span> and all small real <span><math><mi>α</mi></math></span>, improving existing results in various directions, including requiring weaker boundary regularity for the case of the classical 2-Robin problem, studied in the fundamental work by René Sperb. In exterior domains, we characterize the existence of eigenvalues, establish general inequalities and asymptotics as <span><math><mrow><mi>α</mi><mo>→</mo><mn>0</mn></mrow></math></span> for the first eigenvalue of the exterior of a ball, and obtain some sharp geometric inequalities for convex domains in two dimensions.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113943"},"PeriodicalIF":1.3,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157798","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":"Eigenvalues of nonlinear (p,q)-fractional Laplace operator under nonlocal Neumann conditions","authors":"Pierre Aime Feulefack ,&nbsp;Emmanuel Wend-Benedo Zongo","doi":"10.1016/j.na.2025.113949","DOIUrl":"10.1016/j.na.2025.113949","url":null,"abstract":"<div><div>In this paper, we investigate on a bounded open set of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> with smooth boundary, an eigenvalue problem involving a sum of nonlocal operators <span><math><mrow><msubsup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msubsup><mo>+</mo><msubsup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>q</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msubsup></mrow></math></span> with <span><math><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>p</mi><mo>,</mo><mi>q</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span> and subject to the corresponding homogeneous nonlocal <span><math><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>-Neumann boundary condition. A careful analysis of the considered problem leads us to a complete description of the set of eigenvalues as being the precise interval <span><math><mrow><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow><mo>∪</mo><mrow><mo>(</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mi>q</mi><mo>)</mo></mrow><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span> is the first nonzero eigenvalue of the homogeneous fractional <span><math><mi>q</mi></math></span>-Laplacian under nonlocal <span><math><mi>q</mi></math></span>-Neumann boundary condition. Due to the nonlocal feature of the operators appearing in the equations, some purely nonlocal situations occur and bring in a difference in the study of nonlocal problems compared to local ones. Furthermore, we establish that every eigenfunctions is globally bounded.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113949"},"PeriodicalIF":1.3,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157796","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":"Stability of positive radial steady states for the parabolic Hénon–Lane–Emden system","authors":"Daniel Devine ,&nbsp;Paschalis Karageorgis","doi":"10.1016/j.na.2025.113945","DOIUrl":"10.1016/j.na.2025.113945","url":null,"abstract":"<div><div>When it comes to the nonlinear heat equation <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msup></mrow></math></span>, the stability of positive radial steady states in the supercritical case was established in the classical paper by Gui, Ni and Wang. We extend this result to systems of reaction–diffusion equations by studying the positive radial steady states of the parabolic Hénon–Lane–Emden system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>Δ</mi><mi>u</mi></mtd><mtd><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></mrow><mrow><mi>k</mi></mrow></msup><msup><mrow><mi>v</mi></mrow><mrow><mi>p</mi></mrow></msup></mtd><mtd><mtext>in</mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>Δ</mi><mi>v</mi></mtd><mtd><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></mrow><mrow><mi>l</mi></mrow></msup><msup><mrow><mi>u</mi></mrow><mrow><mi>q</mi></mrow></msup></mtd><mtd><mtext>in</mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>k</mi><mo>,</mo><mi>l</mi><mo>≥</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>p</mi><mo>,</mo><mi>q</mi><mo>≥</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mi>p</mi><mi>q</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>. Assume that <span><math><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span> lies either on or above the Joseph–Lundgren critical curve which arose in the work of Chen, Dupaigne and Ghergu. Then all positive radial steady states have the same asymptotic behavior at infinity, and they are all stable solutions of the parabolic Hénon–Lane–Emden system in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113945"},"PeriodicalIF":1.3,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157797","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}