Journal of Differential Equations最新文献

{"title":"Expansiveness, generators and Lyapunov exponents for finitely generated monoid actions","authors":"Xiaojun Huang ,&nbsp;Yu Liu","doi":"10.1016/j.jde.2025.113469","DOIUrl":"10.1016/j.jde.2025.113469","url":null,"abstract":"<div><div>In this paper, we generalize the results of Fathi by establishing that a compact metrizable space admits an expansive finitely generated monoid action if, and only if, it possesses a compatible hyperbolic metric. Furthermore, we demonstrate the equivalence of the concepts of expansiveness, increasing small distances, and expanding small distances within a rather general framework. Additionally, we affirm that a compact metrizable space admits an expansive countable group action precisely when it has a generator. Moreover, we prove that the expansiveness property of group actions is inherited by finite-index subgroups and finite extensions. Lastly, we exhibit that the Lyapunov exponents for an expansive system are necessarily nonzero, thereby indicating that such a system exhibits chaotic behavior. Concurrently, we also demonstrate that negative Lyapunov exponents for compact invariant sets of a dynamical system imply that the compact set in question functions as an attractor.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"440 ","pages":"Article 113469"},"PeriodicalIF":2.4,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169145","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":"Oscillation theory for linear evolution processes","authors":"M.Ap. Silva ,&nbsp;E.M. Bonotto ,&nbsp;M. Federson","doi":"10.1016/j.jde.2025.113464","DOIUrl":"10.1016/j.jde.2025.113464","url":null,"abstract":"<div><div>We introduce the theory of pullback oscillation for linear evolution processes. Necessary and sufficient conditions are presented to obtain pullback oscillation via geometric interpretation of the closed conic hull. Using the theory of generalized ODEs, we apply the main results to a class of abstract ordinary differential equations, as well as to Volterra-Stieltjes-type integral equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"440 ","pages":"Article 113464"},"PeriodicalIF":2.4,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169295","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":"Singularly perturbed Hopf boundary equilibrium of planar piecewise smooth vector fields","authors":"Tiago Carvalho ,&nbsp;Luiz Fernando Gonçalves ,&nbsp;Bruno Rodrigues Freitas","doi":"10.1016/j.jde.2025.113454","DOIUrl":"10.1016/j.jde.2025.113454","url":null,"abstract":"<div><div>In this paper, we describe, via singular perturbations and blow-ups, the dynamics around a boundary equilibrium of planar piecewise smooth vector fields. After all desingularizations, we show that the singularly perturbed system has asymptotically attractor equilibria as the <em>ω</em>-limit set.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"440 ","pages":"Article 113454"},"PeriodicalIF":2.4,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144154441","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":"Hopf bifurcation of three-dimensional systems with parameters","authors":"Ai Ke ,&nbsp;Maoan Han","doi":"10.1016/j.jde.2025.113463","DOIUrl":"10.1016/j.jde.2025.113463","url":null,"abstract":"<div><div>In this paper, we study Hopf bifurcation of limit cycles for a class of three-dimensional systems with multiple parameters. We develop two methods to determine the number of limit cycles near the origin. We also provide two application examples, obtaining some new results on the number of limit cycles in Hopf bifurcation.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"440 ","pages":"Article 113463"},"PeriodicalIF":2.4,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144146698","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":"Concavity and perturbed concavity for p-Laplace equations","authors":"Marco Gallo,&nbsp;Marco Squassina","doi":"10.1016/j.jde.2025.113452","DOIUrl":"10.1016/j.jde.2025.113452","url":null,"abstract":"<div><div>In this paper we study convexity properties for quasilinear Lane-Emden-Fowler equations of the type<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><mi>u</mi><mo>=</mo><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>q</mi></mrow></msup></mtd><mtd><mspace></mspace><mtext> in Ω</mtext><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>&gt;</mo><mn>0</mn></mtd><mtd><mspace></mspace><mtext> in Ω</mtext><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn></mtd><mtd><mspace></mspace><mtext> on ∂Ω</mtext><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> when <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> is a convex domain. In particular, in the subhomogeneous case <span><math><mi>q</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>]</mo></math></span>, the solution <em>u</em> inherits concavity properties from <em>a</em> whenever assumed, while it is proved to be concave up to an error if <em>a</em> is near to a constant. More general problems are also taken into account, including a wider class of nonlinearities. These results generalize some contained in <span><span>[91]</span></span> and <span><span>[120]</span></span>.</div><div>Additionally, some results for the singular case <span><math><mi>q</mi><mo>∈</mo><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></span> and the superhomogeneous case <span><math><mi>q</mi><mo>&gt;</mo><mi>p</mi><mo>−</mo><mn>1</mn></math></span>, <span><math><mi>q</mi><mo>≈</mo><mi>p</mi><mo>−</mo><mn>1</mn></math></span> are obtained. Some properties for the <em>p</em>-fractional Laplacian <span><math><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>p</mi></mrow><mrow><mi>s</mi></mrow></msubsup></math></span>, <span><math><mi>s</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>, <span><math><mi>s</mi><mo>≈</mo><mn>1</mn></math></span>, are shown as well.</div><div>We highlight that some results are new even in the semilinear framework <span><math><mi>p</mi><mo>=</mo><mn>2</mn></math></span>; in some of these cases, we deduce also uniqueness (and nondegeneracy) of the critical point of <em>u</em>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"440 ","pages":"Article 113452"},"PeriodicalIF":2.4,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144146697","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 method to determine the minimal null control time of 1D linear hyperbolic balance laws","authors":"Long Hu ,&nbsp;Guillaume Olive","doi":"10.1016/j.jde.2025.113455","DOIUrl":"10.1016/j.jde.2025.113455","url":null,"abstract":"<div><div>In this paper we introduce a method to find the minimal control time for the null controllability of 1D first-order linear hyperbolic systems by one-sided boundary controls when the coefficients are regular enough.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"440 ","pages":"Article 113455"},"PeriodicalIF":2.4,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144146696","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":"Helmholtz quasi-resonances are unstable under most single-signed perturbations of the wave speed","authors":"Euan A. Spence ,&nbsp;Jared Wunsch ,&nbsp;Yuzhou Zou","doi":"10.1016/j.jde.2025.113441","DOIUrl":"10.1016/j.jde.2025.113441","url":null,"abstract":"<div><div>We consider Helmholtz problems with a perturbed wave speed, where the single-signed perturbation is linear in a parameter <em>z</em>. Both the wave speed and the perturbation are allowed to be discontinuous (modelling a penetrable obstacle). We show that there exists a polynomial function of frequency such that, for any frequency, for most values of <em>z</em>, the norm of the solution operator is bounded by that function.</div><div>This solution-operator bound is most interesting for Helmholtz problems with strong trapping; recall that here there exists a sequence of real frequencies, tending to infinity, through which the solution operator grows superalgebraically, with these frequencies often called <em>quasi-resonances</em>. The result of this paper then shows that, at every fixed frequency in the quasi-resonance, the norm of the solution operator becomes much smaller for most single-signed perturbations of the wave speed, i.e., quasi-resonances are unstable under most such perturbations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"440 ","pages":"Article 113441"},"PeriodicalIF":2.4,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138250","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":"Rate of convergence for homogenization of nonlinear weakly coupled Hamilton-Jacobi systems","authors":"Hiroyoshi Mitake ,&nbsp;Panrui Ni","doi":"10.1016/j.jde.2025.113442","DOIUrl":"10.1016/j.jde.2025.113442","url":null,"abstract":"<div><div>Here, we study the periodic homogenization problem of nonlinear weakly coupled systems of Hamilton-Jacobi equations in the convex setting. We establish a rate of convergence <span><math><mi>O</mi><mo>(</mo><msqrt><mrow><mi>ε</mi></mrow></msqrt><mo>)</mo></math></span> which is sharp.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"440 ","pages":"Article 113442"},"PeriodicalIF":2.4,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134804","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 strongly degenerate fully nonlinear mean field game with nonlocal diffusion","authors":"Indranil Chowdhury ,&nbsp;Espen R. Jakobsen ,&nbsp;Miłosz Krupski","doi":"10.1016/j.jde.2025.113436","DOIUrl":"10.1016/j.jde.2025.113436","url":null,"abstract":"<div><div>There are few results on mean field game (MFG) systems where the PDEs are either fully nonlinear or have degenerate diffusions. This paper introduces a problem that combines both difficulties. We prove existence and uniqueness for a strongly degenerate, fully nonlinear MFG system by using the well-posedness theory for fully nonlinear MFGs established in our previous paper <span><span>[23]</span></span>. It is the first such application in a degenerate setting. Our MFG involves a controlled pure jump (nonlocal) Lévy diffusion of order less than one, and monotone, smoothing couplings. The key difficulty is obtaining uniqueness for the corresponding Fokker–Planck equation which has degenerate, non-Lipschitz, and low regularity diffusion coefficients: since the regularity of the coefficient and the order of the diffusion are interdependent, it holds when the order is sufficiently low. Viscosity solutions and a non-standard doubling of variables argument are used along with a bootstrapping procedure.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"440 ","pages":"Article 113436"},"PeriodicalIF":2.4,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134854","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":"Heat kernel bounds and Cheng-Yau type estimate for the Laplace-Beltrami operator with Bakry-Émery Ricci curvature lower bound","authors":"XingYu Song ,&nbsp;Ling Wu ,&nbsp;Meng Zhu","doi":"10.1016/j.jde.2025.113439","DOIUrl":"10.1016/j.jde.2025.113439","url":null,"abstract":"<div><div>On complete Riemannian manifolds with Bakry-Émery Ricci curvature bounded below, we first derive a parabolic Harnack inequality for positive solutions of the heat equation and Gaussian upper and lower bounds of the heat kernel for the Laplace-Beltrami operator. As applications of the heat kernel estimates, an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-Liouville theorem for non-negative subharmonic functions and lower bounds of the Dirichlet eigenvalues are shown. Finally, we prove Cheng-Yau type local gradient estimates for positive harmonic functions and Dirichlet and Neumann eigenfunctions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"440 ","pages":"Article 113439"},"PeriodicalIF":2.4,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134648","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}