Journal of Differential Equations最新文献

{"title":"Solutions with prescribed mass for the p-Laplacian Schrödinger-Poisson system with critical growth","authors":"Kai Liu , Xiaoming He , Vicenţiu D. Rădulescu","doi":"10.1016/j.jde.2025.113570","DOIUrl":"10.1016/j.jde.2025.113570","url":null,"abstract":"<div><div>In this paper, we focus on the existence and multiplicity of solutions for the <em>p</em>-Laplacian Schrödinger-Poisson system<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>γ</mi><mi>ϕ</mi><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>=</mo><mi>λ</mi><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>μ</mi><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mrow><msup><mrow><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo></mtd><mtd><mspace></mspace><mspace></mspace><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>ϕ</mi><mo>=</mo><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mo>,</mo></mtd><mtd><mspace></mspace><mspace></mspace><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> with a prescribed mass given by<span><span><span><math><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></munder><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mi>d</mi><mi>x</mi><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>,</mo></math></span></span></span> in the Sobolev critical case, where, <span><math><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mn>3</mn><mo>,</mo><mi>a</mi><mo>></mo><mn>0</mn></math></span>, and <span><math><mi>γ</mi><mo>></mo><mn>0</mn></math></span>, <span><math><mi>μ</mi><mo>></mo><mn>0</mn></math></span> are parameters, <span><math><msup><mrow><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>=</mo><mfrac><mrow><mn>3</mn><mi>p</mi></mrow><mrow><mn>3</mn><mo>−</mo><mi>p</mi></mrow></mfrac></math></span> is the Sobolev critical exponent, and <span><math><mi>λ</mi><mo>∈</mo><mi>R</mi></math></span> is an undetermined parameter, acting as a Lagrange multiplier. We investigate this system under the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-subcritical perturbation <span><math><mi>μ</mi><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi></math></span>, with <span><math><mi>q</mi><mo>∈</mo><mo>(</mo><mi>p</mi><mo>,</mo><mi>p</mi><mo>+</mo><mfrac><mrow><msup><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>3</mn></mrow></mfrac><mo>)</mo></math></span>, and establish the existence of multiple normalized solutions using the truncation technique, concentration-compactness ","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"444 ","pages":"Article 113570"},"PeriodicalIF":2.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490447","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-source type atmospheric nonlinear flow patterns in zonal cloud bands","authors":"C.I. Martin","doi":"10.1016/j.jde.2025.113589","DOIUrl":"10.1016/j.jde.2025.113589","url":null,"abstract":"<div><div>We present a family of exact solutions to a set of recently derived nonlinear equations governing at leading order the dynamics of flows in zonal cloud bands that resemble those on Jupiter. These solutions are radial in the horizontal variables, present density and temperature that decrease with height, a pressure function that decreases in the radial direction, and allow heat flowing out into the environment: these are features that are also observed in the Jupiter's Red Spot. Using a WKB analysis we show that certain exact solutions are stable under a specific choice of the density distribution.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"445 ","pages":"Article 113589"},"PeriodicalIF":2.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490405","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":"Sharp lifespan estimates for semilinear fractional evolution equations with critical nonlinearity","authors":"Wenhui Chen ,&nbsp;Giovanni Girardi","doi":"10.1016/j.jde.2025.113568","DOIUrl":"10.1016/j.jde.2025.113568","url":null,"abstract":"<div><div>In this paper we consider semilinear wave equation and semilinear second order <em>σ</em>-evolution equations with different (effective or non-effective) damping mechanisms driven by fractional Laplace operators; in particular, the nonlinear term is the product of a power nonlinearity <span><math><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup></math></span> with the critical exponent <span><math><mi>p</mi><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math></span> and a modulus of continuity <span><math><mi>μ</mi><mo>(</mo><mo>|</mo><mi>u</mi><mo>|</mo><mo>)</mo></math></span>. We derive a critical condition on the nonlinearity by proving a global in time existence result under the Dini condition on <em>μ</em> and a blow-up result when <em>μ</em> does not satisfy the Dini condition. Especially, in this latter case we determine new sharp estimates for the lifespan of local solutions, obtaining coincident upper and lower bounds of the lifespan. In particular, we derive a new sharp estimate for the wave equation with structural damping and classical power nonlinearity <span><math><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup></math></span> in the critical case <span><math><mi>p</mi><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math></span>, not yet determined in previous literature. The proof of the blow-up results and the upper bound estimates of the lifespan require the introduction of new test functions which allows to overcome some new difficulties due to the presence of both non-local differential operators and general nonlinearities.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113568"},"PeriodicalIF":2.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144491147","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 and large-time behavior for Euler-like equations","authors":"Jiahong Wu ,&nbsp;Xiaojing Xu ,&nbsp;Yueyuan Zhong ,&nbsp;Ning Zhu","doi":"10.1016/j.jde.2025.113578","DOIUrl":"10.1016/j.jde.2025.113578","url":null,"abstract":"<div><div>This paper intends to understand the long-time existence and stability of solutions to an Euler-like equation. An Euler-like equation is the 2D incompressible Euler equation with an extra singular integral operator (SIO) type term. In contrast to the 2D Euler equation, the vorticity to the 2D Euler-like equation is not known to be bounded due to the unboundedness of the SIO on the space <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>. As a consequence, classical Yudovich theory fails on the Euler-like equation. The global existence, regularity and stability problems on the Euler-like equation are generally open. This paper makes progress on an Euler-like equation arising in the study of several fluids. We establish a long-time existence and stability result. When the Sobolev size of the initial data is of order <em>ε</em>, the solution is shown to live on a time interval of the size <span><math><mn>1</mn><mo>/</mo><msup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. When the initial data is restricted to a class with special symmetry, we obtain the global existence and nonlinear stability.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"444 ","pages":"Article 113578"},"PeriodicalIF":2.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144491342","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":"Regularity of the 3D stochastic viscous Primitive Equations","authors":"Zhao Dong ,&nbsp;Hao Xiong ,&nbsp;Guoli Zhou","doi":"10.1016/j.jde.2025.113579","DOIUrl":"10.1016/j.jde.2025.113579","url":null,"abstract":"<div><div>Utilizing the method of hydrostatic decomposition, we obtain the smoothness property and uniform <em>a</em> <span><math><mi>p</mi><mi>r</mi><mi>i</mi><mi>o</mi><mi>r</mi><mi>i</mi></math></span> estimates for the strong solution to 3D stochastic Primitive Equations (PEs) of large-scale ocean and atmosphere dynamics with non-periodic condition. Consequently, we derive the existence of invariant measures and the smoothness of random attractor.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"445 ","pages":"Article 113579"},"PeriodicalIF":2.4,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144480526","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 stability of traveling waves for Nagumo equations with degenerate diffusion","authors":"Tianyuan Xu ,&nbsp;Shanming Ji ,&nbsp;Ming Mei ,&nbsp;Jingxue Yin","doi":"10.1016/j.jde.2025.113587","DOIUrl":"10.1016/j.jde.2025.113587","url":null,"abstract":"<div><div>This paper is concerned with the global nonlinear stability with possibly large perturbations of the unique sharp / smooth traveling waves for the degenerate diffusion equations with Nagumo (bistable) reaction. Two technical issues arise in this study. One is the shortage of weak regularity of sharp traveling waves, the other difficulty is the non-absorbing initial-perturbation around the smooth traveling waves at the far field <span><math><mi>x</mi><mo>=</mo><mo>+</mo><mo>∞</mo></math></span>. For the sharp traveling wave case, we technically construct weak sub- and super-solutions with semi-compact supports via translation and scaling of the unique sharp traveling wave to characterize the motion of the steep moving edges and avoid the weak regularity of the solution near the steep edges. For the smooth traveling wave case, we artfully combine both the translation and scaling type sub- and super-solutions and the translation and superposition type sub- and super-solutions in a systematical manner.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"445 ","pages":"Article 113587"},"PeriodicalIF":2.4,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490352","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":"Isolated singularities of solutions of linear and semilinear elliptic equations with singular drifts","authors":"Hyunseok Kim","doi":"10.1016/j.jde.2025.113574","DOIUrl":"10.1016/j.jde.2025.113574","url":null,"abstract":"<div><div>We study isolated singularities of solutions of linear and semilinear elliptic equations in divergence form with singular drifts. First, extending a classical result for isolated singularities of harmonic functions, we establish a removable isolated singularity theorem for linear equations with drifts <strong>b</strong> in <span><math><msup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>q</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msup><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>R</mi></mrow></msub><mtext>; </mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> for some <span><math><msub><mrow><mi>q</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≥</mo><mi>n</mi></math></span>, where <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span> is the dimension. Then this theorem is applied to prove removability theorems for isolated singularities of solutions of some semilinear equations with drifts in <span><math><msup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>q</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msup><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>R</mi></mrow></msub><mtext>; </mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>. One novelty of our results is that the critical case <span><math><msub><mrow><mi>q</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mi>n</mi></math></span> is allowed for removable singularity theorems for both linear and semilinear equations. Moreover, our methods of proofs rely only on interior <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>q</mi></mrow></msup></math></span>-estimates for solutions on annuli and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span>-estimates for their traces on spheres but not pointwise estimates like the maximum principle, which can be thus applied to linear and nonlinear systems.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"444 ","pages":"Article 113574"},"PeriodicalIF":2.4,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471820","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":"Kato-Ponce inequality for fractional nonlocal parabolic operators","authors":"Meng Qu ,&nbsp;Xinfeng Wu","doi":"10.1016/j.jde.2025.113572","DOIUrl":"10.1016/j.jde.2025.113572","url":null,"abstract":"<div><div>We establish Kato-Ponce inequality (or fractional Leibniz rule) for fractional nonlocal parabolic operators <span><math><msup><mrow><mo>(</mo><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><msub><mrow><mo>△</mo></mrow><mrow><mi>x</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>s</mi><mo>/</mo><mn>2</mn></mrow></msup></math></span> and <span><math><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><msub><mrow><mo>△</mo></mrow><mrow><mi>x</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>s</mi><mo>/</mo><mn>2</mn></mrow></msup></math></span> of arbitrary order <span><math><mi>s</mi><mo>&gt;</mo><mn>0</mn></math></span> for a full range of Lebesgue indices including the endpoints, and determine the sharp range of <em>s</em>. We also prove a sharp Kato-Ponce commutator inequality for <span><math><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><msub><mrow><mo>△</mo></mrow><mrow><mi>x</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>s</mi><mo>/</mo><mn>2</mn></mrow></msup></math></span>. To achieve these results, we not only adapt the methods of Bourgain-Li <span><span>[11]</span></span>, Grafakos-Oh <span><span>[25]</span></span> and Oh-Wu <span><span>[50]</span></span> to the present parabolic setting, but build up sharp decay estimates for higher-order hyper-singular integrals of Nogin-Rubin <span><span>[48]</span></span> and Stinga-Torrea <span><span>[54]</span></span>, which are crucial for us to derive the sharp ranges of <em>s</em>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113572"},"PeriodicalIF":2.4,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144470604","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":"Transport equations for Osgood velocity fields","authors":"U.S. Fjordholm,&nbsp;O. Mæhlen","doi":"10.1016/j.jde.2025.113566","DOIUrl":"10.1016/j.jde.2025.113566","url":null,"abstract":"<div><div>We consider the transport equation with a velocity field satisfying the Osgood condition. The weak formulation is not meaningful in the usual Lebesgue sense, meaning that the usual DiPerna–Lions treatment of the problem is not applicable (in particular, the divergence of the velocity might be unbounded). Instead, we use Riemann–Stieltjes integration to interpret the weak formulation, leading to a well-posedness theory in regimes not covered by existing works. The most general results are for the one-dimensional problem, with generalisations to multiple dimensions in the particular case of log-Lipschitz velocities.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113566"},"PeriodicalIF":2.4,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144470603","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":"Low regularity results for degenerate Poisson problems","authors":"Marta Calanchi ,&nbsp;Massimo Grossi","doi":"10.1016/j.jde.2025.113567","DOIUrl":"10.1016/j.jde.2025.113567","url":null,"abstract":"<div><div>In this paper we study the Poisson problem,<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mo>−</mo><mrow><mi>div</mi></mrow><mo>(</mo><msup><mrow><mi>d</mi></mrow><mrow><mi>β</mi></mrow></msup><mi>∇</mi><mi>u</mi><mo>)</mo><mo>=</mo><mi>f</mi></mtd><mtd><mrow><mi>in</mi></mrow><mspace></mspace><mi>Ω</mi></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn></mtd><mtd><mrow><mi>on</mi></mrow><mspace></mspace><mo>∂</mo><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> where <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>, <span><math><mi>N</mi><mo>≥</mo><mn>2</mn></math></span> is a smooth bounded domain, <em>f</em> is a continuous function, <span><math><mi>β</mi><mo>&lt;</mo><mn>1</mn></math></span>, and <span><math><mi>d</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>d</mi><mi>i</mi><mi>s</mi><mi>t</mi><mo>(</mo><mi>x</mi><mo>,</mo><mo>∂</mo><mi>Ω</mi><mo>)</mo></math></span>. We describe the behaviour of <em>u</em> near ∂Ω and discuss some of its regularity properties.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113567"},"PeriodicalIF":2.4,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144470605","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}