Nonlinear Analysis-Theory Methods & Applications最新文献

英文中文

A sharp volume inequality for mixed LYZ ellipsoids 混合LYZ椭球体的尖锐体积不等式

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-05-01 Epub Date: 2025-12-16 DOI: 10.1016/j.na.2025.114036

Sitao Zhang

Based on the concept of mixed LYZ ellipsoid and the technique of isotropic embedding, a sharp reverse affine isoperimetric inequality is established in this paper. This inequality is a generalization of a weak version of the Mahler conjecture obtained by Lutwak, Yang, and Zhang [31].

基于混合LYZ椭球的概念和各向同性嵌入技术，建立了一个尖锐逆仿射等周不等式。这个不等式是由Lutwak， Yang和Zhang所得到的马勒猜想的弱版本的推广。

引用次数: 0

Generalized existence of extremizers for the sharp p-Sobolev inequality on Riemannian manifolds with nonnegative curvature 黎曼非负曲率流形上尖锐p-Sobolev不等式极值的广义存在性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-05-01 Epub Date: 2025-12-04 DOI: 10.1016/j.na.2025.114029

Francesco Nobili, Ivan Yuri Violo

We study the generalized existence of extremizers for the sharp p-Sobolev inequality on noncompact Riemannian manifolds in connection with nonnegative curvature and Euclidean volume growth assumptions. Assuming a nonnegative Ricci curvature lower bound, we show that almost extremal functions are close in gradient norm to radial Euclidean bubbles. In the case of nonnegative sectional curvature lower bounds, we additionally deduce that vanishing is the only possible behavior, in the sense that almost extremal functions are almost zero globally. Our arguments rely on nonsmooth concentration compactness methods and Mosco-convergence results for the Cheeger energy on noncompact varying spaces, generalized to every exponent p ∈ (1, ∞).

研究了非紧黎曼流形上尖锐p-Sobolev不等式在非负曲率和欧几里德体积增长条件下极值的广义存在性。假设一个非负的里奇曲率下界，我们证明了几乎极值函数在梯度范数上接近径向欧几里得气泡。在非负截面曲率下界的情况下，我们进一步推导出消失是唯一可能的行为，在某种意义上，几乎极值函数在全局上几乎为零。我们的论点依赖于非紧变空间上Cheeger能量的非光滑集中紧性方法和莫斯科收敛结果，推广到每一个指数p ∈ （1,∞）。

引用次数: 0

Nonlocal ordered mean curvature with integrable kernels 具有可积核的非局部有序平均曲率

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-05-01 Epub Date: 2025-12-09 DOI: 10.1016/j.na.2025.114028

Animesh Biswas , Mikil D. Foss , Petronela Radu

In this paper we introduce and study the concept of nonlocal ordered curvature. In the classical (differential) setting, the problem was introduced by Li and Nirenberg in [1, 2] where they conjectured (and proved in some cases) that if a bounded smooth surface has its mean curvature ordered in a particular direction, then the surface must be symmetric with respect to some hyperplane orthogonal to that direction. The conjecture was finally settled by Li et al in 2021 [3]. Here we study the counterpart problem in the nonlocal setting, where the nonlocal mean curvature of a set Ω, at any point x on its boundary, is defined as

H_{Ω}^{J} (x) = \int_{Ω^{c}} J (x - y) d y - \int_{Ω} J (x - y) d y

and the kernel function J is radially symmetric, non-increasing, integrable and compactly supported. Using a generalization of Alexandrov’s moving plane method, we prove a similar result in the nonlocal setting.

本文引入并研究了非局部有序曲率的概念。在经典（微分）设置中，Li和Nirenberg在[1,2]中引入了这个问题，他们推测（并在某些情况下证明），如果有界光滑表面的平均曲率在特定方向上有序，那么该表面必须相对于与该方向正交的某个超平面对称。这个猜想最终在2021年由Li等人解决。本文研究了非局部环境下的对应问题，其中集Ω在其边界任意点x处的非局部平均曲率定义为HΩJ(x)=∫ΩcJ(x−y)dy -∫ΩJ(x−y)dy，核函数J是径向对称的、不增加的、可积的和紧支持的。利用Alexandrov移动平面方法的推广，我们证明了在非局部情况下的类似结果。

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引用次数: 0

Radially symmetric solutions of nonlocal elliptic equations on the unit ball 单位球上非局部椭圆方程的径向对称解

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-05-01 Epub Date: 2025-12-18 DOI: 10.1016/j.na.2025.114040

Tianlan Chen , Christopher S. Goodrich

We consider a class of nonlocal elliptic PDEs, of which one model case is the steady-state Kirchhoff-type equation

- {M (∥ D u ∥}_{L^{p}}^{p}) Δ u (x) = λ f (| x |, u (x)), x \in B_{1},

where

B_{1}

is the unit ball in

R^{n}

, where n ≥ 2. Under the assumption that u satisfies Dirichlet boundary datum on

\partial B_{1}

, we demonstrate existence of at least one positive radially symmetric solution to the PDE by means of topological fixed point theory. Our results are valid both in the low-dimensional setting (n < p) and the high-dimensional setting (n ≥ p), though the techniques required differ between the two cases. The existence arguments utilise a specialised order cone.

考虑一类非局部椭圆型偏微分方程，其中一种模型情况为稳态kirchhoff型方程−M（∥Du∥Lpp）Δu(x)=λf(|x|,u(x)),x∈B1，其中B1为Rn中的单位球，其中n ≥ 2。在假设u满足∂B1上的Dirichlet边界基准的前提下，利用拓扑不动点理论证明了PDE存在至少一个正的径向对称解。我们的结果在低维环境（n <； p）和高维环境（n ≥ p）下都是有效的，尽管这两种情况所需的技术有所不同。存在性论证使用了一个特殊的顺序锥。

引用次数: 0

On minima of lattice energy under Yukawa potentials 汤川势作用下晶格能的极小值

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-05-01 Epub Date: 2025-12-26 DOI: 10.1016/j.na.2025.114045

Chen-Gang Long , Senping Luo , Wenming Zou

In this paper, we consider the minimization problem of two dimensional lattice energy

\min_{| Λ | = 1} E_{f} (Λ), where E_{f} (Λ) = \sum_{P \in Λ ∖ {0}} {f (| P |}^{2}) .

We study this minimization problem under the classical Yukawa potential

f (r) = \frac{e^{- α π r}}{r} - β \frac{e^{- t α π r}}{r}

with α > 0, t > 1 and

β \in R

. We prove the existence of a critical value

β_{c} = 1

such that:

•
if $β \in (- \infty, β_{c}],$ then the minimizer corresponds to a hexagonal lattice configuration;
•
if $β \in (β_{c}, + \infty),$ then no minimizer exists.

This result provide the sharp bound β_c for hexagonal lattice crystallization under Yukawa potential. Furthermore, we extend the analysis to two-component lattices, where each component is centered on the other, and obtain the same critical value β_c. In this case, the minimizer transitions between a rhombic-square-rectangular configuration and a scenario where no minimizer exists.

本文考虑二维点阵能量min|Λ|=1Ef（Λ）的最小化问题，其中ef （Λ）=∑P∈Λ∈{0}f（|P|2）。我们研究了经典汤川势f(r)=e - απrr - βe - tαπrr, α >； 0,t >； 1，β∈r条件下的最小化问题。证明了一个临界值βc=1的存在性，使得：•如果β∈(−∞,βc)，则最小值对应于六边形晶格构型；•如果β∈(βc,+∞)，则不存在最小值。这一结果提供了汤川势作用下六方晶格结晶的锐界βc。进一步，我们将分析扩展到双分量格，其中每个分量都以另一个分量为中心，并得到相同的临界值βc。在这种情况下，最小化器在菱形平方矩形配置和不存在最小化器的场景之间转换。

引用次数: 0

Global existence and large-time behavior of spherically symmetric solutions for a viscous heat-conducting ionized gas in exterior domains 粘性热传导电离气体外域球对称解的整体存在性和大时性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-05-01 Epub Date: 2025-12-05 DOI: 10.1016/j.na.2025.114031

Hao Chen , Yongkai Liao , Ling Wan

We study global-in-time spherically symmetric solutions for a viscous, compressible, heat-conducting ionized gas in a n-dimensional unbounded exterior domain with large initial data, where n ≥  2 is the space dimension. The properties of ionized gases, combined with the unboundedness of the exterior domain, make it challenging to estimate the first-order spatial derivatives of the bulk velocity and the absolute temperature. For a class of constant non-vacuum equilibrium states, we obtain the uniform-in-time bounds on the dissipative estimates for both the bulk velocity and the absolute temperature. Based on such estimates, we establish the global existence and asymptotic behavior of spherically symmetric solutions to the viscous and heat-conducting ionized gas in unbounded exterior domains with large initial data. The key point lies in deducing the lower and upper bounds on the specific volume and the temperature.

本文研究了具有大初始数据的n维无界外域中粘性、可压缩、热传导电离气体的全局时球对称解，其中n ≥ 2为空间维数。电离气体的性质，加上外域的无界性，使得估计体积速度和绝对温度的一阶空间导数变得很困难。对于一类恒定非真空平衡态，我们得到了体速度和绝对温度的耗散估计的等时界。在此基础上，我们建立了具有大初始数据的粘性热电离气体在无界外域球对称解的整体存在性和渐近性。关键在于推导出比容和温度的上下边界。

引用次数: 0

The blow-up dynamics for the divergence Schrödinger equations with inhomogeneous nonlinearity 非齐次非线性散度Schrödinger方程的爆破动力学

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-04-01 Epub Date: 2025-11-24 DOI: 10.1016/j.na.2025.114015

Bowen Zheng , Tohru Ozawa

<div><div>This paper is dedicated to the blow-up solution for the divergence Schrödinger equations with inhomogeneous nonlinearity (dINLS for short) <span><span><span><math><mrow><mi>i</mi><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>+</mo><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><msup><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></mrow><mrow><mi>b</mi></mrow></msup><mo>∇</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><msup><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></mrow><mrow><mi>c</mi></mrow></msup><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi></mrow></msup><mi>u</mi><mo>,</mo><mspace></mspace><mspace></mspace><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mn>2</mn><mo>−</mo><mi>n</mi><mo><</mo><mi>b</mi><mo><</mo><mn>2</mn></mrow></math></span>, <span><math><mrow><mi>c</mi><mo>></mo><mi>b</mi><mo>−</mo><mn>2</mn></mrow></math></span> and <span><math><mrow><mi>n</mi><mi>p</mi><mo>−</mo><mn>2</mn><mi>c</mi><mo><</mo><mrow><mo>(</mo><mn>2</mn><mo>−</mo><mi>b</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>p</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>. First, for radial blow-up solutions in <span><math><msubsup><mrow><mi>W</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msubsup></math></span>, we prove an upper bound on the blow-up rate for the intercritical dNLS. Moreover, an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm concentration in the mass-critical case is also obtained by giving a compact lemma. Next, we turn to the non-radial case. By establishing two types of Gagliardo–Nirenberg inequalities, we show the existence of finite time blow-up solutions in <span><math><mrow><msup><mrow><mover><mrow><mi>H</mi></mrow><mrow><mo>̇</mo></mrow></mover></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></msup><mo>∩</mo><msubsup><mrow><mover><mrow><mi>W</mi></mrow><mrow><mo>̇</mo></mrow></mover></mrow><mrow><mi>b</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msubsup></mrow></math></span>, where <span><math><mrow><msup><mrow><mover><mrow><mi>H</mi></mrow><mrow><mo>̇</mo></mrow></mover></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></msup><mo>=</mo><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mfrac><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span> and <span><math><mrow><msubsup><mrow><mover><mrow><mi>W</mi></mrow><mrow><mo>̇</mo></mrow></mover></mrow><mrow><mi>b</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msubsup

本文研究具有非齐次非线性（dINLS） i∂tu+∇⋅(|x|b∇u)= - |x|c|u|pu,u(x,0)=u0(x)的散度Schrödinger方程的爆破解，其中2 - n<；b<2, c>；b - 2和np - 2c<；（2 - b）（p+2）。首先，对于Wb1,2中的径向爆破解，我们证明了临界间dNLS爆破率的上界。此外，通过给出一个紧引理，还得到了质量临界情况下的l2范数浓度。接下来，我们转向非径向情况。通过建立两种类型的Gagliardo-Nirenberg不等式，我们证明了Ḣsc∩Ẇb1,2中有限时间爆炸解的存在性，其中Ḣsc=（−Δ）−sc2L2和Ẇb1,2=|x|−b2（−Δ）−12L2。作为一个应用，我们得到了这个爆破率的下界，将Merle和Raphaël（2008）对经典NLS方程的工作推广到dINLS设置。

引用次数: 0

Keplerian billiards in three dimensions: Stability of equilibrium orbits and conditions for chaos 三维的开普勒台球：平衡轨道的稳定性和混沌的条件

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-04-01 Epub Date: 2025-11-20 DOI: 10.1016/j.na.2025.114018

Irene De Blasi

This work presents some results regarding three-dimensional billiards having a non-constant potential of Keplerian type inside a regular domain

D \subset R^{3}

. Two models will be analysed: in the first one, only an inner Keplerian potential is present, and every time the particle encounters the boundary of

D

is reflected back by keeping constant its tangential component to

\partial D

, while the normal one changes its sign. The second model is a refractive billiard, where the inner Keplerian potential is coupled with a harmonic outer one; in this case, the interaction with

\partial D

results in a generalised refraction Snell’s law. In both cases, the analysis of a particular type of straight equilibrium trajectories, called homothetic, is carried on, and their presence is linked to the topological chaoticity of the dynamics for large inner energies.

这项工作提出了关于在正则域D∧R3内具有开普勒型非恒定势的三维台球的一些结果。将分析两个模型：在第一个模型中，只有一个内开普勒势存在，并且每次粒子遇到D的边界时，通过保持其切向分量与∂D不变而反射回来，而法向分量则改变其符号。第二个模型是一个折射台球，其中内部的开普勒势与外部的谐波势耦合；在这种情况下，与∂D的相互作用产生广义折射斯涅尔定律。在这两种情况下，对一种称为同质的特殊类型的直线平衡轨迹进行了分析，并且它们的存在与大内能动力学的拓扑混沌性有关。

引用次数: 0

Exotic traveling waves for a quasilinear Schrödinger equation with nonzero background 具有非零背景的拟线性Schrödinger方程的奇异行波

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-04-01 Epub Date: 2025-11-30 DOI: 10.1016/j.na.2025.114027

André de Laire, Erwan Le Quiniou

We study a defocusing quasilinear Schrödinger equation with nonzero conditions at infinity in dimension one. This quasilinear model corresponds to a weakly nonlocal approximation of the nonlocal Gross–Pitaevskii equation, and can also be derived by considering the effects of surface tension in superfluids. When the quasilinear term is neglected, the resulting equation is the classical Gross–Pitaevskii equation, which possesses a well-known stable branch of subsonic traveling waves solution, given by dark solitons.

Our goal is to investigate how the quasilinear term and the intensity-dependent dispersion affect the traveling-wave solutions. We provide a complete classification of finite energy traveling waves of the equation, in terms of two parameters: the speed and the strength of the quasilinear term. This classification leads to the existence of dark and antidark solitons, as well as more exotic localized solutions like dark cuspons, compactons, and composite waves, even for supersonic speeds. Depending on the parameters, these types of solutions can coexist, showing that finite energy solutions are not unique. Furthermore, we prove that some of these dark solitons can be obtained as minimizers of the energy, at fixed momentum, and that they are orbitally stable.

研究了一维无穷远处具有非零条件的离焦拟线性Schrödinger方程。该拟线性模型对应于非局部Gross-Pitaevskii方程的弱非局部近似，也可以通过考虑超流体中表面张力的影响来推导。当忽略拟线性项时，得到的方程是经典的Gross-Pitaevskii方程，该方程具有众所周知的由暗孤子给出的亚音速行波解的稳定分支。我们的目标是研究拟线性项和强度相关色散如何影响行波解。我们给出了有限能量行波方程的完整分类，根据两个参数：速度和拟线性项的强度。这种分类导致了暗孤子和反暗孤子的存在，以及更奇特的局部解，如暗垫子、紧子和复合波，甚至对于超音速也是如此。根据参数的不同，这些类型的解可以共存，这表明有限能量解不是唯一的。此外，我们证明了其中一些暗孤子可以作为能量的最小值，在固定动量下获得，并且它们是轨道稳定的。

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引用次数: 0

On the existence of optimal and ɛ-optimal controls for the stochastic 2D nonlocal Cahn–Hilliard–Navier–Stokes system 关于二维随机非局部Cahn-Hilliard-Navier-Stokes系统的最优控制和最优控制的存在性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-04-01 Epub Date: 2025-11-19 DOI: 10.1016/j.na.2025.114016

R.D. Ayissi , G. Deugoué , J. Ngandjou Zangue , T. Tachim Medjo

In this paper, we study a feedback optimal control problem for the stochastic nonlocal Cahn–Hilliard–Navier–Stokes model in a two-dimensional bounded domain. The model consists of the stochastic Navier–Stokes equations for the velocity, coupled with a nonlocal Cahn-Hilliard system for the order (phase) parameter. We prove the existence of an optimal feedback control for the stochastic nonlocal Cahn–Hilliard-Navier-Stokes system. Moreover using the Galerkin approximation, we show that the optimal cost can be approximated by a sequence of finite dimensional optimal costs.

本文研究了二维有界区域上随机非局部Cahn-Hilliard-Navier-Stokes模型的反馈最优控制问题。该模型由速度的随机Navier-Stokes方程和阶（相位）参数的非局部Cahn-Hilliard系统组成。证明了随机非局部Cahn-Hilliard-Navier-Stokes系统的最优反馈控制的存在性。此外，利用伽辽金近似，我们证明了最优成本可以用有限维最优成本序列来逼近。

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全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

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