Nonlinear Analysis-Theory Methods & Applications最新文献

英文中文

Existence of multiple solutions for the generalized abelian Chern–Simons–Higgs model on a torus 环面上广义阿贝尔chen - simons - higgs模型的多重解的存在性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-09-25 DOI: 10.1016/j.na.2025.113950

Jongmin Han, Kyungwoo Song

We construct multiple solutions of the generalized self-dual abelian Chern–Simons–Higgs equation in a two-dimensional flat torus by the topological degree method.

利用拓扑度方法构造了二维平面环面上广义自对偶阿贝耳chen - simons - higgs方程的多个解。

引用次数: 0

Behavior of absorbing and generating p-Robin eigenvalues in bounded and exterior domains 有界域和外域吸收和生成p-Robin特征值的行为

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-09-24 DOI: 10.1016/j.na.2025.113943

Lukas Bundrock, Tiziana Giorgi, Robert Smits

We establish rigorous quantitative inequalities for the first eigenvalue of the generalized

p

-Robin problem, for both the classical diffusion absorption case, where the Robin boundary parameter

α

is positive, and the superconducting generation regime (

α < 0

), where the boundary acts as a source. In bounded domains, we use a unified approach to derive a precise asymptotic behavior for all

p

and all small real

α

, improving existing results in various directions, including requiring weaker boundary regularity for the case of the classical 2-Robin problem, studied in the fundamental work by René Sperb. In exterior domains, we characterize the existence of eigenvalues, establish general inequalities and asymptotics as

α \to 0

for the first eigenvalue of the exterior of a ball, and obtain some sharp geometric inequalities for convex domains in two dimensions.

我们建立了广义p-Robin问题的第一特征值的严格定量不等式，适用于经典扩散吸收情况，其中Robin边界参数α为正，以及超导产生区（α<0），其中边界作为源。在有界域中，我们使用统一的方法推导了所有p和所有小实α的精确渐近行为，在各个方向上改进了现有的结果，包括在ren Sperb的基础工作中研究的经典2-Robin问题的情况下需要较弱的边界正则性。在外域上，我们刻画了特征值的存在性，建立了球外第一个特征值的一般不等式和渐近性为α→0，得到了二维凸域上的尖锐几何不等式。

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引用次数: 0

Eigenvalues of nonlinear (p,q)-fractional Laplace operator under nonlocal Neumann conditions 非局部诺伊曼条件下非线性（p,q）分数阶拉普拉斯算子的特征值

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-09-24 DOI: 10.1016/j.na.2025.113949

Pierre Aime Feulefack , Emmanuel Wend-Benedo Zongo

In this paper, we investigate on a bounded open set of

R^{N}

with smooth boundary, an eigenvalue problem involving a sum of nonlocal operators

{(- Δ)}_{p}^{s_{1}} + {(- Δ)}_{q}^{s_{2}}

with

s_{1}, s_{2} \in (0, 1)

p, q \in (1, \infty)

and subject to the corresponding homogeneous nonlocal

(p, q)

-Neumann boundary condition. A careful analysis of the considered problem leads us to a complete description of the set of eigenvalues as being the precise interval

{0} \cup (λ_{1} (s_{2}, q), \infty)

, where

λ_{1} (s_{2}, q)

is the first nonzero eigenvalue of the homogeneous fractional

q

-Laplacian under nonlocal

q

-Neumann boundary condition. Due to the nonlocal feature of the operators appearing in the equations, some purely nonlocal situations occur and bring in a difference in the study of nonlocal problems compared to local ones. Furthermore, we establish that every eigenfunctions is globally bounded.

在光滑边界的有界开集RN上，研究了一个涉及非局部算子（−Δ）ps1+（−Δ）qs2的和的特征值问题，其中s1，s2∈(0,1),p,q∈(1,∞)，并满足相应的齐次非局部(p,q)-Neumann边界条件。通过对所考虑问题的仔细分析，我们得到了特征值集是精确区间{0}∪(λ1(s2,q),∞)的完整描述，其中λ1（s2,q）是齐次分数阶q- laplace在非局部q- neumann边界条件下的第一个非零特征值。由于方程中出现的算子的非局部特性，导致了一些纯非局部情况的出现，使得非局部问题的研究与局部问题的研究有了很大的不同。进一步证明了每个特征函数是全局有界的。

引用次数: 0

Stability of positive radial steady states for the parabolic Hénon–Lane–Emden system 抛物型hsamnon - lane - emden系统正径向稳态的稳定性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-09-24 DOI: 10.1016/j.na.2025.113945

Daniel Devine , Paschalis Karageorgis

When it comes to the nonlinear heat equation

u_{t} - Δ u = u^{p}

, the stability of positive radial steady states in the supercritical case was established in the classical paper by Gui, Ni and Wang. We extend this result to systems of reaction–diffusion equations by studying the positive radial steady states of the parabolic Hénon–Lane–Emden system

(\begin{matrix} u_{t} - Δ u & = {| x |}^{k} v^{p} & in R^{n} \times (0, \infty), \\ v_{t} - Δ v & = {| x |}^{l} u^{q} & in R^{n} \times (0, \infty), \end{matrix})

where

k, l \geq 0

p, q \geq 1

and

p q > 1

. Assume that

(p, q)

lies either on or above the Joseph–Lundgren critical curve which arose in the work of Chen, Dupaigne and Ghergu. Then all positive radial steady states have the same asymptotic behavior at infinity, and they are all stable solutions of the parabolic Hénon–Lane–Emden system in

R^{n}

对于非线性热方程ut−Δu=up， Gui、Ni和Wang在经典论文中建立了超临界情况下径向正稳态的稳定性。通过研究抛物型h - lane - emden系统ut−Δu=|x| kvpinrnx(0,∞),vt−Δv=|x| luqinrnx(0,∞)，其中k，l≥0,p,q≥1,pq>；1的正径向稳态，我们将这一结果推广到反应扩散方程系统。假设（p,q）位于Joseph-Lundgren临界曲线上或之上，该曲线由Chen、Dupaigne和Ghergu提出。那么所有正径向稳态在无穷远处都具有相同的渐近性质，它们都是Rn中抛物型h - lane - emden系统的稳定解。

引用次数: 0

Existence and nonexistence of solutions for weighted elliptic inequalities involving gradient terms 涉及梯度项的加权椭圆不等式解的存在性与不存在性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-09-24 DOI: 10.1016/j.na.2025.113951

Roberta Filippucci , Yadong Zheng

In this paper we prove existence and nonexistence theorems for positive solutions of elliptic inequalities for general quasilinear operators, including

m

-Laplacian, mean curvature and generalized mean curvature operator, in the entire

R^{N}

with a reaction involving power type gradient terms and positive weights, possibly singular or degenerate. A complete picture for the exponents involved is given. The proof technique is based on cumbersome integral a priori estimates, in the spirit of the nonlinear capacity method. No maximum principle or growth conditions at infinity for the solutions are required.

本文证明了一般拟线性算子（包括m-拉普拉斯算子、平均曲率算子和广义平均曲率算子）在整个RN上的椭圆不等式正解的存在性和不存在性定理，其反应涉及幂型梯度项和正权，可能是奇异的或简并的。给出了所涉及的指数的全貌。证明技术是基于繁琐的积分先验估计，在非线性容量方法的精神。不需要解在无穷远处的极大值原理或增长条件。

引用次数: 0

On the existence of periodic solutions for damped asymmetric oscillators 非对称阻尼振子周期解的存在性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-09-20 DOI: 10.1016/j.na.2025.113946

Alessandro Fonda , Giuliano Klun , Andrea Sfecci

We propose some new sufficient conditions for the existence of periodic solutions of an asymmetric oscillator with a positive damping term. Our results are complemented by an example where, in some situations, no periodic solutions may exist. This fact is well known in the undamped case, when the resonance phenomenon may appear. However, the damped case presents some unintuitive features which have not been so thoroughly studied in the literature, and the overall picture still has several aspects which need to be better understood.

给出了具有正阻尼项的非对称振子周期解存在的几个新的充分条件。我们的结果得到了一个例子的补充，在某些情况下，周期解可能不存在。这一事实在无阻尼情况下是众所周知的，当共振现象可能出现时。然而，阻尼情况表现出一些不直观的特征，这些特征在文献中尚未得到如此深入的研究，总体情况仍有几个方面需要更好地理解。

引用次数: 0

SBV functions in Carnot–Carathéodory spaces SBV在carnot - carath<s:1>空间中的作用

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-09-17 DOI: 10.1016/j.na.2025.113944

Marco Di Marco , Sebastiano Don , Davide Vittone

We introduce the space SBV

_{X}

of special functions with bounded

X

-variation in Carnot–Carathéodory spaces and study its main properties. Our main outcome is an approximation result, with respect to the BV

_{X}

topology, for SBV

_{X}

functions.

引入了carnot - carathacimodory空间中具有有界x变分的特殊函数的空间SBVX，并研究了其主要性质。我们的主要结果是关于SBVX函数的BVX拓扑的近似结果。

引用次数: 0

Some results on g-stability for hypersurfaces in an initial data set 关于初始数据集超曲面g稳定性的一些结果

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-09-16 DOI: 10.1016/j.na.2025.113914

A.B. Lima , R.M. Batista , P.A. Sousa

We study the

g

-stability of hypersurfaces

Σ^{n - 1}

with null expansion

θ^{+} = h \geq 0

in an

n

-dimensional initial data set

M^{n}

with cosmological constant

Λ

. First, under natural energy conditions, we demonstrate that

Σ^{n - 1} \subset M^{n}

admits a metric with positive scalar curvature. Second, for a

g

-stable surface

Σ^{2}

of genus

g (Σ)

, we establish an inequality relating the area of

Σ

, its genus,

Λ

, and the charge

q (Σ)

. Moreover, if equality holds and

Λ > 0

Σ^{2}

is a round 2-sphere. Finally, for a

g

-stable, two-sided, closed hypersurface

Σ^{4}

in a 5-dimensional initial data set

M^{5}

satisfying natural energy conditions, we derive an inequality involving the area of

Σ

, its charge

q (Σ)

, and a positive constant depending on the total traceless Ricci curvature of

Σ

. Equality implies that

Σ^{4}

is isometric to

S^{4}

在具有宇宙常数Λ的n维初始数据集Mn中，研究了零展开θ+=h≥0的超曲面Σn−1的g稳定性。首先，在自然能量条件下，我们证明Σn−1∧Mn允许一个具有正标量曲率的度规。其次，对于g属稳定曲面Σ2 （Σ），我们建立了一个关于Σ、其属、Λ和电荷q（Σ）的面积的不等式。此外，如果等式成立并且Λ>；0，则Σ2是一个圆的2球。最后，对于满足自然能量条件的5维初始数据集M5中的g稳定的双面封闭超曲面Σ4，我们导出了一个不等式，该不等式涉及Σ的面积，其电荷q（Σ）和依赖于Σ的总无迹Ricci曲率的正常数。等式表明Σ4与S4等长。

引用次数: 0

On least energy solutions for a nonlinear Schrödinger system with K-wise interaction 具有K-wise相互作用的非线性Schrödinger系统的最小能量解

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-09-12 DOI: 10.1016/j.na.2025.113938

Lorenzo Giaretto, Nicola Soave

In this paper we establish existence and properties of minimal energy solutions for the weakly coupled system

(\begin{matrix} - Δ u_{i} + λ_{i} u_{i} = μ_{i} | u_{i} |^{K q - 2} u_{i} + β | u_{i} |^{q - 2} u_{i} \prod_{j \neq i} | u_{j} |^{q} in R^{d} \\ u_{i} \in H^{1} (R^{d}), \end{matrix}) i = 1, \dots, K,

characterized by

K

-wise interaction (namely the interaction term involves the product of all the components). We consider both attractive (

β > 0

) and repulsive cases (

β < 0

), and we give sufficient conditions on

β

in order to have least energy fully non-trivial solutions, if necessary under a radial constraint. We also study the asymptotic behaviour of least energy fully non-trivial radial solutions in the limit of strong competition

β \to - \infty

, showing partial segregation phenomena which differ substantially from those arising in pairwise interaction models.

本文建立了弱耦合系统- Δui+λiui=μi|ui|Kq−2ui+β|ui|q−2ui∏j≠i|uj|qinRdui∈H1(Rd),i=1，…，K的最小能量解的存在性和性质，其特征为K-wise相互作用（即相互作用项涉及所有分量的乘积）。我们考虑了吸引（β>0）和排斥（β<0）两种情况，并给出了β的充分条件，以便在径向约束下得到能量最小的完全非平凡解。我们还研究了在强竞争β→−∞极限下最小能量完全非平凡径向解的渐近行为，显示出与两两相互作用模型中出现的部分偏析现象有很大不同。

引用次数: 0

Minimization of the first positive eigenvalue for the beam equation with indefinite weight 带不定权的梁方程第一个正特征值的最小化

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2025-09-11 DOI: 10.1016/j.na.2025.113933

Yu Gan , Zhaowen Zheng , Kun Li , Jing Shao

In this paper, we obtain the sharp estimate of the first positive eigenvalue for the beam equation

y^{(4)} (t) = - λ m (t) y (t)

with Lidstone boundary condition, where weight function

m

is allowed to change sign. We first establish a variational characterization for the first positive eigenvalue of the measure differential equation (MDE)

d y^{(3)} (t) = - λ y (t) d μ (t),

and solve the corresponding minimization problem of the first positive eigenvalue for the MDE, where

μ

is a suitable measure. Then by finding the relationship between minimization problem for the first positive eigenvalue of ordinary differential equation (ODE) and that of MDE, we obtain the explicit sharp lower bound of the first positive eigenvalue for the indefinite beam equation.

本文在允许权函数m变符号的Lidstone边界条件下，得到了梁方程y(4)(t)= - λm(t)y(t)的第一正特征值的尖锐估计。首先建立测度微分方程（MDE） dy(3)(t)= - λy(t)dμ(t)的第一个正特征值的变分刻画，并求解了该测度微分方程（MDE）的第一个正特征值的最小化问题，其中μ是合适的测度。然后通过找出常微分方程（ODE）的第一个正特征值最小化问题与MDE的第一个正特征值最小化问题之间的关系，得到了不定梁方程的第一个正特征值的显式尖锐下界。

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引用次数: 0

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