Journal of Differential Equations最新文献

{"title":"Two positive normalized solutions on star-shaped bounded domains to the Brézis-Nirenberg problem","authors":"Linjie Song,&nbsp;Wenming Zou","doi":"10.1016/j.jde.2026.114169","DOIUrl":"10.1016/j.jde.2026.114169","url":null,"abstract":"<div><div>We establish the existence of two positive solutions with prescribed mass for NLS on star-shaped bounded domains: one is the normalized ground state and another is at a mountain pass level. We merely address the Sobolev critical case since the Sobolev subcritical one can be addressed by following similar arguments and is easier.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"460 ","pages":"Article 114169"},"PeriodicalIF":2.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146090557","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 Calderón-Zygmund type theory for elliptic problems with degenerate weights from composite structures","authors":"Yumi Cho ,&nbsp;Yunsoo Jang","doi":"10.1016/j.jde.2026.114147","DOIUrl":"10.1016/j.jde.2026.114147","url":null,"abstract":"<div><div>In this research, we study a higher regularity result for elliptic problems with degenerate weights. We consider nonlinear <em>p</em>-Laplacian type elliptic equations related to composite materials which are composed of two or more distinct substances with different properties. Under the suitable assumptions on the nonlinearities and the geometry of composite structures, we obtain a global Calderón-Zygmund type theory.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"460 ","pages":"Article 114147"},"PeriodicalIF":2.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146090700","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":"Modulus of continuity for depinning force at rational rotation symbols and application","authors":"Wen-Xin Qin ,&nbsp;Tong Zhou","doi":"10.1016/j.jde.2025.114092","DOIUrl":"10.1016/j.jde.2025.114092","url":null,"abstract":"<div><div>The depinning force for the Frenkel-Kontorova chain is a critical value <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>(</mo><mi>ω</mi><mo>)</mo></math></span> of the driving force <em>F</em> up to which there continue to be Birkhoff equilibria of rotation symbol <em>ω</em> and above which there are none. In this paper we investigate the modulus of continuity for the depinning force at rational rotation symbols <span><math><mi>p</mi><mo>/</mo><mi>q</mi><mo>+</mo></math></span> and <span><math><mi>p</mi><mo>/</mo><mi>q</mi><mo>−</mo></math></span> and obtain the estimate<span><span><span><math><mo>|</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>(</mo><mi>p</mi><mo>/</mo><mi>q</mi><mo>+</mo><mo>)</mo><mo>−</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>(</mo><mi>ω</mi><mo>)</mo><mo>|</mo><mo>≤</mo><mi>C</mi><mo>|</mo><mi>q</mi><msup><mrow><mi>ω</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>−</mo><mi>p</mi><mo>|</mo><mo>,</mo><mspace></mspace><mtext> for </mtext><mspace></mspace><mi>ω</mi><mo>&gt;</mo><mi>p</mi><mo>/</mo><mi>q</mi><mo>+</mo><mo>,</mo></math></span></span></span> where <em>C</em> is a constant and <span><math><msup><mrow><mi>ω</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> denotes the underlying number associated to the rotation symbol <em>ω</em>. A similar conclusion for <span><math><mi>p</mi><mo>/</mo><mi>q</mi><mo>−</mo></math></span> also holds true.</div><div>As an application, we give an open and dense result for <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>(</mo><mn>0</mn><mo>/</mo><mn>1</mn><mo>+</mo><mo>)</mo><mo>&gt;</mo><mn>0</mn></math></span>, a threshold of driving force such that there exist stationary fronts for <span><math><mi>F</mi><mo>≤</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>(</mo><mn>0</mn><mo>/</mo><mn>1</mn><mo>+</mo><mo>)</mo></math></span> and traveling fronts for <span><math><mi>F</mi><mo>&gt;</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>(</mo><mn>0</mn><mo>/</mo><mn>1</mn><mo>+</mo><mo>)</mo></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"460 ","pages":"Article 114092"},"PeriodicalIF":2.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145977972","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":"Slowly oscillating periodic solutions in a nonlinear Volterra equation with non-symmetric feedback","authors":"Quentin Griette ,&nbsp;Franco Herrera","doi":"10.1016/j.jde.2025.114071","DOIUrl":"10.1016/j.jde.2025.114071","url":null,"abstract":"<div><div>In this work we study a nonlinear Volterra equation with non-symmetric feedback that arises as a particular case of the Gurtin-MacCamy model in population dynamics. We are particularly interested in the existence of slowly oscillating periodic solutions when the trivial stationary state is unstable. Here the absence of symmetry of the nonlinearity prevents the use of many traditional strategies to obtain a priori estimates on the solution. Without a precise knowledge of the period of the solution, we manage to prove the forward invariance of a carefully constructed set of initial data whose properties imply the slowly oscillating character of all continuations. We prove the existence of periodic solutions by constructing a homeomorphism between our set and a convex subset of a different Banach space, thereby showing that it possesses the fixed-point property. Finally, in a singular limit of a parameter, we show that this periodic solution converges to the solution of a well-known discrete difference equation. We conclude the paper with some numerical simulations to illustrate the existence of the periodic orbit as well as the singular limit behavior.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"460 ","pages":"Article 114071"},"PeriodicalIF":2.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940022","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 existence for full compressible Navier-Stokes equations around the Couette flow with a temperature gradient in an infinite channel","authors":"Tuowei Chen ,&nbsp;Qiangchang Ju","doi":"10.1016/j.jde.2026.114095","DOIUrl":"10.1016/j.jde.2026.114095","url":null,"abstract":"<div><div>This paper is concerned with the two-dimensional full compressible Navier-Stokes equations between two infinite parallel isothermal walls, where the upper wall is moving with a horizontal velocity, while the lower wall is stationary, and there allows a temperature difference between the two walls. It is shown that if the initial state is close to the Couette flow with a temperature gradient, then the global strong solutions exist, provided that the Reynolds and Mach numbers are low and the temperature difference between the two walls is small. The low Mach number limit of the global strong solutions is also shown for the case that both walls maintain the same temperature.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"460 ","pages":"Article 114095"},"PeriodicalIF":2.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145977973","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":"Dynamical versions of Morgan's uncertainty principle and electromagnetic Schrödinger evolutions","authors":"Shanlin Huang ,&nbsp;Zhenqiang Wang","doi":"10.1016/j.jde.2026.114159","DOIUrl":"10.1016/j.jde.2026.114159","url":null,"abstract":"<div><div>This paper investigates the unique continuation properties of solutions of the electromagnetic Schrödinger equation<span><span><span><math><mi>i</mi><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>+</mo><msup><mrow><mo>(</mo><mi>∇</mi><mo>−</mo><mi>i</mi><mi>A</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mtext>in</mtext><mspace></mspace><mspace></mspace><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>×</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo><mo>,</mo></math></span></span></span> where <em>A</em> represents a time-independent magnetic vector potential and <em>V</em> is a bounded, complex valued time-dependent potential. Given <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mn>2</mn></math></span> and <span><math><mn>1</mn><mo>/</mo><mi>p</mi><mo>+</mo><mn>1</mn><mo>/</mo><mi>q</mi><mo>=</mo><mn>1</mn></math></span>, we prove that there exists <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>&gt;</mo><mn>0</mn></math></span> such that if<span><span><span><math><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></munder><mo>|</mo><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><msup><mrow><mi>α</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mo>/</mo><mi>p</mi></mrow></msup><mi>d</mi><mi>x</mi><mo>+</mo><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></munder><mo>|</mo><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>1</mn><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><msup><mrow><mi>β</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi></mrow></msup><mo>/</mo><mi>q</mi></mrow></msup><mi>d</mi><mi>x</mi><mo>&lt;</mo><mo>∞</mo></math></span></span></span> for some <span><math><mi>α</mi><mo>,</mo><mi>β</mi><mo>&gt;</mo><mn>0</mn></math></span>, and if <span><math><mi>α</mi><mi>β</mi><mo>&gt;</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>, then <span><math><mi>u</mi><mo>≡</mo><mn>0</mn></math></span>. These results can be interpreted as dynamical versions of the uncertainty principle of Morgan's type. Furthermore, as an application, our results extend to a large class of semi-linear Schrödinger equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"460 ","pages":"Article 114159"},"PeriodicalIF":2.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146090558","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 new proof of the Cp′-conjecture in the plane via a priori estimates","authors":"Genival da Silva","doi":"10.1016/j.jde.2025.114058","DOIUrl":"10.1016/j.jde.2025.114058","url":null,"abstract":"<div><div>In this note, we present an alternative proof that weak solutions to<span><span><span><math><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><mi>u</mi><mo>=</mo><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></math></span></span></span> belong to <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>l</mi><mi>o</mi><mi>c</mi></mrow><mrow><msup><mrow><mi>p</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span>, where <span><math><mi>p</mi><mo>&gt;</mo><mn>2</mn></math></span> and <span><math><mi>Ω</mi><mo>⊆</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. The first complete proof of this result was given in <span><span>[1]</span></span>; here, we give an alternative argument.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"460 ","pages":"Article 114058"},"PeriodicalIF":2.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145802213","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":"Principal Bautin ideal of monodromic singularities with inverse integrating factors","authors":"Isaac A. García,&nbsp;Jaume Giné","doi":"10.1016/j.jde.2025.114069","DOIUrl":"10.1016/j.jde.2025.114069","url":null,"abstract":"<div><div>We analyze the structure of the Poincaré map Π associated to a monodromic singularity of an analytic family of planar vector fields. We work under two assumptions. The first one is that the family possesses an inverse integrating factor that can be expanded in Laurent series centered at the singularity after a weighted polar blow-up fixed by the Newton diagram of the family. The second one is that we restrict our analysis to a subset of the monodromic parameter space that assures the non-existence of local curves with zero angular speed. The conclusions are that the asymptotic Dulac expansion of Π does not contain logarithmic terms, indeed it admits a formal power series expansion with a unique independent generalized Poincaré-Lyapunov quantity, which can be computed under some explicit conditions. Moreover we also give conditions that guarantee the analyticity of Π, in which case we show that the Bautin ideal is principal and therefore the cyclicity of the singularity with respect to perturbation within the family is zero.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"460 ","pages":"Article 114069"},"PeriodicalIF":2.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882139","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":"Spectral stability of elliptic function solutions for the short pulse equation","authors":"Li-Ming Cao,&nbsp;Shou-Fu Tian","doi":"10.1016/j.jde.2026.114099","DOIUrl":"10.1016/j.jde.2026.114099","url":null,"abstract":"<div><div>The main purpose of this work is to investigate the spectral stability of elliptic function solutions for the short pulse equation, a completely integrable model for the description of ultra-short pulse propagation in optical fibers. Recently, Yang and Fan developed <span><math><mover><mrow><mo>∂</mo></mrow><mrow><mo>¯</mo></mrow></mover></math></span>-steepest descent method to analyze the long-time asymptotic behavior for the short pulse equation (Yang and Fan (2021) <span><span>[50]</span></span>). Subsequently, Li, Tian and Yang extended their results and reported the asymptotic stability of N-soliton solution (Li et al. (2023) <span><span>[33]</span></span>). Inspired by these works, we consider the spectral stability for three classes of elliptic solutions which are derived via the algebraic geometry method in this work. It is worth noting that the Lax spectrum in focusing case is not restricted to imaginary axis. To address this issue, we develop the squared wavefunction method using Jacobi theta function theory, and then establish spectral stability for both focusing and defocusing cases.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"460 ","pages":"Article 114099"},"PeriodicalIF":2.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145977971","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":"Large time behavior of solutions to unipolar Euler-Poisson equations with space-dependent damping","authors":"Chunpeng Wang,&nbsp;Jianing Xu","doi":"10.1016/j.jde.2026.114172","DOIUrl":"10.1016/j.jde.2026.114172","url":null,"abstract":"<div><div>This paper is concerned with the Cauchy problem to Euler-Poisson equations for one-dimensional unipolar hydrodynamic model of semiconductors with damping of space-dependent coefficient. Under some smallness assumptions on the initial data, we establish the global existence of smooth solutions to the Cauchy problem by applying the energy methods. It is shown that the solutions to unipolar Euler-Poisson equations with space-dependent damping time-exponentially converge to the stationary solutions. No smallness assumption is imposed on the space-dependent coefficient of damping.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"460 ","pages":"Article 114172"},"PeriodicalIF":2.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146090559","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}