Journal of Differential Equations最新文献

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Two positive normalized solutions on star-shaped bounded domains to the Brézis-Nirenberg problem brsamzis - nirenberg问题在星形有界区域上的两个正规范化解

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-04-15 Epub Date: 2026-01-30 DOI: 10.1016/j.jde.2026.114169

Linjie Song, Wenming Zou

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.

我们建立了星形有界域上NLS的两个规定质量正解的存在性：一个是归一化基态，另一个是在山口水平。我们只讨论Sobolev临界情况，因为Sobolev次临界情况可以通过类似的论证来解决，而且更容易。

引用次数: 0

Global Calderón-Zygmund type theory for elliptic problems with degenerate weights from composite structures 复合结构退化权椭圆型问题的全局Calderón-Zygmund型理论

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-04-15 Epub Date: 2026-01-27 DOI: 10.1016/j.jde.2026.114147

Yumi Cho , Yunsoo Jang

In this research, we study a higher regularity result for elliptic problems with degenerate weights. We consider nonlinear p-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.

本文研究了具有退化权值的椭圆型问题的一个高正则性结果。考虑由两种或两种以上性质不同的物质组成的复合材料的非线性p-拉普拉斯型椭圆方程。在适当的非线性和复合结构几何假设下，我们得到了一个全局Calderón-Zygmund型理论。

引用次数: 0

Modulus of continuity for depinning force at rational rotation symbols and application 合理旋转符号下脱紧力的连续模量及其应用

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-04-15 Epub Date: 2026-01-13 DOI: 10.1016/j.jde.2025.114092

Wen-Xin Qin , Tong Zhou

The depinning force for the Frenkel-Kontorova chain is a critical value

F_{d} (ω)

of the driving force F up to which there continue to be Birkhoff equilibria of rotation symbol ω and above which there are none. In this paper we investigate the modulus of continuity for the depinning force at rational rotation symbols

p / q +

and

p / q -

and obtain the estimate

| F_{d} (p / q +) - F_{d} (ω) | \leq C | q ω^{⁎} - p |, for ω > p / q +,

where C is a constant and

ω^{⁎}

denotes the underlying number associated to the rotation symbol ω. A similar conclusion for

p / q -

also holds true.

As an application, we give an open and dense result for

F_{d} (0 / 1 +) > 0

, a threshold of driving force such that there exist stationary fronts for

F \leq F_{d} (0 / 1 +)

and traveling fronts for

F > F_{d} (0 / 1 +)

Frenkel-Kontorova链的脱紧力是驱动力F的临界值Fd(ω)，在此值之前继续存在旋转符号ω的Birkhoff平衡，而在此值以上则不存在。本文研究了有理旋转符号p/q+和p/q−处的沉降力的连续性模量，得到了对ω>；p/q+的估计|Fd(p/q+) - Fd(ω)|≤C|qω - p|，其中C为常数，ω表示与旋转符号ω相关的底层数。p/q−的类似结论也成立。作为应用，我们给出了Fd(0/1+)>；0的一个开放而密集的结果，一个驱动力阈值使得F≤Fd（0/1+）存在平稳锋，F>Fd（0/1+）存在行进锋。

引用次数: 0

Slowly oscillating periodic solutions in a nonlinear Volterra equation with non-symmetric feedback 非对称反馈非线性Volterra方程的慢振荡周期解

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-04-15 Epub Date: 2026-01-05 DOI: 10.1016/j.jde.2025.114071

Quentin Griette , Franco Herrera

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.

在这项工作中，我们研究了具有非对称反馈的非线性Volterra方程，它是种群动力学中Gurtin-MacCamy模型的一个特殊情况。当平凡的定态不稳定时，我们对慢振荡周期解的存在性特别感兴趣。在这里，非线性的不对称性阻碍了使用许多传统策略来获得对解的先验估计。在没有解周期的精确知识的情况下，我们设法证明了一组精心构造的初始数据的前向不变性，这些初始数据的性质暗示了所有延拓的缓慢振荡特征。通过构造该集合与另一个Banach空间的凸子集之间的同胚，证明了周期解的存在性，从而证明了它具有不动点的性质。最后，在一个参数的奇异极限下，我们证明了这个周期解收敛于一个众所周知的离散差分方程的解。最后用一些数值模拟来说明周期轨道的存在性和奇异极限行为。

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引用次数: 0

Global existence for full compressible Navier-Stokes equations around the Couette flow with a temperature gradient in an infinite channel 具有温度梯度的无限通道内Couette流动的全可压缩Navier-Stokes方程的全局存在性

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-04-15 Epub Date: 2026-01-13 DOI: 10.1016/j.jde.2026.114095

Tuowei Chen , Qiangchang Ju

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.

本文研究了两个无限平行等温壁面之间的二维完全可压缩Navier-Stokes方程，其中上壁面以水平速度运动，下壁面静止，并且两壁面之间存在温差。结果表明，当初始状态接近具有温度梯度的Couette流时，在雷诺数和马赫数较低、两壁温差较小的条件下，存在全局强解。在两壁保持相同温度的情况下，还显示了全局强解的低马赫数极限。

引用次数: 0

Dynamical versions of Morgan's uncertainty principle and electromagnetic Schrödinger evolutions 摩根测不准原理的动力学版本和电磁Schrödinger演化

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-04-15 Epub Date: 2026-01-30 DOI: 10.1016/j.jde.2026.114159

Shanlin Huang , Zhenqiang Wang

This paper investigates the unique continuation properties of solutions of the electromagnetic Schrödinger equation

i \partial_{t} u (x, t) + {(\nabla - i A)}^{2} u (x, t) = V (x, t) u (x, t) in R^{d} \times [0, 1],

where A represents a time-independent magnetic vector potential and V is a bounded, complex valued time-dependent potential. Given

1 < p < 2

and

1 / p + 1 / q = 1

, we prove that there exists

N_{p} > 0

such that if

\int_{R^{d}} | u (x, 0) |^{2} e^{2 α^{p} | x |^{p} / p} d x + \int_{R^{d}} | u (x, 1) |^{2} e^{2 β^{q} | x |^{q} / q} d x < \infty

for some

α, β > 0

, and if

α β > N_{p}

, then

u \equiv 0

. 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.

本文研究了电磁Schrödinger方程i∂tu(x,t)+(∇−iA)2u(x,t)=V(x,t)u(x,t) inrdx[0,1]解的唯一连续性质，其中A表示时无关的磁矢量势，V是有界的复值时相关势。给定1<；p<；2和1/p+1/q=1，我们证明了Np>；0的存在，使得∫Rd|u(x,0) |e2α - p|x|p/pdx+∫Rd|u(x,1)|2e2βq|x|q/qdx<；∞对于某些α，β>0，且αβ>；Np，则u≡0。这些结果可以解释为摩根不确定性原理的动态版本。此外，作为一个应用，我们的结果推广到一类半线性Schrödinger方程。

引用次数: 0

Spectral stability of elliptic function solutions for the short pulse equation 短脉冲方程椭圆函数解的谱稳定性

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-04-15 Epub Date: 2026-01-14 DOI: 10.1016/j.jde.2026.114099

Li-Ming Cao, Shou-Fu Tian

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

\bar{\partial}

-steepest descent method to analyze the long-time asymptotic behavior for the short pulse equation (Yang and Fan (2021) [50]). Subsequently, Li, Tian and Yang extended their results and reported the asymptotic stability of N-soliton solution (Li et al. (2023) [33]). 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.

本文的主要目的是研究用于描述超短脉冲在光纤中传播的完全可积模型——短脉冲方程的椭圆函数解的谱稳定性。最近，Yang和Fan开发了∂¯-最陡下降方法来分析短脉冲方程的长时间渐近行为（Yang和Fan(2021)[50]）。随后，Li、Tian和Yang扩展了他们的结果，报道了n孤子解的渐近稳定性（Li et al.(2023)[33]）。受这些工作的启发，本文研究了用代数几何方法导出的三类椭圆解的谱稳定性。值得注意的是，聚焦情况下的Lax光谱并不局限于虚轴。为了解决这个问题，我们利用Jacobi theta函数理论开发了平方波函数方法，然后建立了聚焦和散焦情况下的光谱稳定性。

引用次数: 0

Principal Bautin ideal of monodromic singularities with inverse integrating factors 具有逆积分因子的单点奇异性的主Bautin理想

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-04-15 Epub Date: 2025-12-29 DOI: 10.1016/j.jde.2025.114069

Isaac A. García, Jaume Giné

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.

我们分析了平面向量场解析族的单点奇点所对应的poincar映射Π的结构。我们在两个假设下工作。首先，族具有一个逆积分因子，可以在族的牛顿图固定的加权极坐标放大后，在以奇点为中心的劳伦级数中展开。第二，我们将分析限制在单参数空间的一个子集上，以保证不存在零角速度的局部曲线。结论是Π的渐近Dulac展开式不包含对数项，它确实允许一个形式的幂级数展开式具有唯一独立的广义poincar - lyapunov量，它可以在某些显式条件下计算。此外，我们还给出了保证Π解析性的条件，在这种情况下，我们证明了包丹理想是主要的，因此奇点相对于族内扰动的循环为零。

引用次数: 0

A new proof of the Cp′-conjecture in the plane via a priori estimates 用先验估计证明了平面上的Cp′-猜想

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-04-15 Epub Date: 2025-12-23 DOI: 10.1016/j.jde.2025.114058

Genival da Silva

In this note, we present an alternative proof that weak solutions to

- Δ_{p} u = f \in L^{\infty} (B_{1})

belong to

C_{l o c}^{p^{'}} (Ω)

, where

p > 2

and

Ω \subseteq R^{2}

. The first complete proof of this result was given in [1]; here, we give an alternative argument.

在本文中，我们给出了−Δpu=f∈L∞(B1)的弱解属于Clocp ' （Ω）的另一种证明，其中p>；2和Ω≠R2。这个结果的第一个完整证明是在2010年给出的；这里，我们给出另一种观点。

引用次数: 0

Large time behavior of solutions to unipolar Euler-Poisson equations with space-dependent damping 具有空间相关阻尼的单极欧拉-泊松方程解的大时间行为

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-04-15 Epub Date: 2026-01-30 DOI: 10.1016/j.jde.2026.114172

Chunpeng Wang, Jianing Xu

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.

本文研究了具有空间依赖系数阻尼的一维单极半导体流体力学模型的欧拉-泊松方程的Cauchy问题。在初始数据的一些较小的假设条件下，利用能量方法建立了柯西问题光滑解的全局存在性。证明了具有空间相关阻尼的单极欧拉-泊松方程的解在时间指数上收敛于平稳解。对阻尼的空间相关系数不作小的假设。

引用次数: 0

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