Nonlinear Analysis-Theory Methods & Applications最新文献

英文中文

Optimal planar immersions of prescribed winding number and Arnold invariants 规定圈数和阿诺德不变量的最优平面浸入

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-02-01 Epub Date: 2025-10-10 DOI: 10.1016/j.na.2025.113942

Anna Lagemann, Heiko von der Mosel

Vladimir Arnold defined three invariants for generic planar immersions, i.e. planar curves whose self-intersections are all transverse double points. We use a variational approach to study these invariants by investigating a suitably truncated knot energy, the tangent-point energy. We prove existence of energy minimizers for each truncation parameter

δ > 0

in a class of immersions with prescribed winding number and Arnold invariants, and establish Gamma convergence of the truncated tangent-point energies to a limiting renormalized tangent-point energy as

δ \to 0

. Moreover, we show that any sequence of minimizers subconverges in

C^{1}

, and the corresponding limit curve has the same topological invariants, self-intersects exclusively at right angles, and minimizes the renormalized tangent-point energy among all curves with right self-intersection angles. In addition, the limit curve is an almost-minimizer for all of the original truncated tangent-point energies as long as the truncation parameter

δ

is sufficiently small. Therefore, this limit curve serves as an “optimal” curve in the class of generic planar immersions with prescribed winding number and Arnold invariants.

Vladimir Arnold定义了一般平面浸入式的三个不变量，即自交均为横向双点的平面曲线。我们使用变分的方法来研究这些不变量，通过研究一个适当截断的结能量，切点能量。在给定圈数和Arnold不变量的浸入式中，证明了每一个截断参数δ>；0的能量极小值的存在性，并建立了截断的切点能量的伽玛收敛到一个极限重归一化切点能量为δ→0。此外，我们还证明了任何最小值序列在C1中都是子收敛的，并且相应的极限曲线具有相同的拓扑不变量，在直角处完全自交，并且在所有自交角为直角的曲线中极小化了的切点能量。此外，只要截断参数δ足够小，对于所有原始截断的切点能量，极限曲线几乎是最小的。因此，该极限曲线可作为具有规定圈数和阿诺德不变量的一般平面浸没的一类“最优”曲线。

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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 : 2026-01-01 Epub 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

Local boundedness for solutions of a class of non-uniformly elliptic anisotropic problems 一类非一致椭圆各向异性问题解的局部有界性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-01-01 Epub Date: 2025-09-03 DOI: 10.1016/j.na.2025.113915

Stefano Biagi , Giovanni Cupini , Elvira Mascolo

We consider a class of energy integrals, associated to nonlinear and non-uniformly elliptic equations, with integrands

f (x, u, ξ)

satisfying anisotropic

p_{i}, q

-growth conditions of the form

\sum_{i = 1}^{n} λ_{i} (x) {| ξ_{i} |}^{p_{i}} \leq f (x, u, ξ) \leq μ (x) ({| ξ |}^{q} + {| u |}^{γ} + 1)

for some exponents

γ \geq q \geq p_{i} > 1

, and non-negative functions

λ_{i}, μ

subject to suitable summability assumptions. We prove the local boundedness of scalar local quasi-minimizers of such integrals.

考虑一类与非线性非一致椭圆方程相关的能量积分，其积分f（x,u,ξ）满足各向异性pi，q的增长条件：∑i=1nλi(x)|ξi|pi≤f(x,u,ξ)≤μ(x)|ξ|q+|u|γ+1，对于某些指数γ≥q≥pi>；1，非负函数λi，μ服从适当的可和性假设。证明了这类积分的标量局部拟极小值的局部有界性。

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 : 2026-01-01 Epub 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

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 : 2026-01-01 Epub 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

Hopf’s lemmas and boundary behavior of solutions to the fractional Laplacian in Orlicz-Sobolev spaces Orlicz-Sobolev空间分数阶拉普拉斯算子解的Hopf引理和边界行为

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-01-01 Epub Date: 2025-08-20 DOI: 10.1016/j.na.2025.113923

Pablo Ochoa , Ariel Salort

In this article we study different extensions of the celebrated Hopf’s boundary lemma within the context of a family of nonlocal, nonlinear and nonstandard growth operators. More precisely, we examine the behavior of solutions of the fractional

a

-Laplacian operator near the boundary of a domain satisfying the interior ball condition. Our approach addresses problems involving both constant-sign and sign-changing potentials.

本文在一类非局部、非线性和非标准生长算子的背景下，研究了著名的Hopf边界引理的不同推广。更确切地说，我们研究了分数阶a-拉普拉斯算子在满足内球条件的区域边界附近的解的行为。我们的方法解决了涉及常符号和变符号势的问题。

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 : 2026-01-01 Epub 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

Convergence of normalizations for partially integrable differential systems 部分可积微分系统的归一化收敛性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-01-01 Epub Date: 2025-08-06 DOI: 10.1016/j.na.2025.113902

Wenyong Huang , Valery G. Romanovski , Xiang Zhang

This paper provides some criteria to characterize convergence of normalizations which transform partially integrable analytic differential systems to their Poincaré–Dulac normal forms. For a family of four-dimensional partially integrable differential systems near an equilibrium which has one pair of conjugate imaginary eigenvalues and a pair of resonant nonzero real eigenvalues, we prove convergence of their normalizations. For analytic differential systems with dimension larger than 4, we illustrate that partial integrability may not be sufficient to ensure convergence of the normalizations even though Bruno’s condition

ω

holds. This work generalizes in a natural way the classical results by Poincaré and Lyapunov for a monodromic equilibrium, as well as the one by Moser for a hyperbolic saddle of analytic Hamiltonian systems of one degree of freedom.

本文给出了部分可积解析微分系统转化为庞加莱姆-杜拉克范式的归一化收敛性的几个判据。对于一类具有一对共轭虚特征值和一对共振非零实特征值的四维部分可积微分系统，证明了它们的归一化的收敛性。对于维数大于4的解析微分系统，即使Bruno条件ω成立，部分可积性也不足以保证归一化的收敛性。这项工作以一种自然的方式推广了庞加莱和李亚普诺夫关于单平衡点的经典结果，以及莫泽关于一自由度解析哈密顿系统双曲鞍的经典结果。

引用次数: 0

Ideal magnetohydrodynamics around couette flow: Long time stability and vorticity–current instability 库埃特流周围的理想磁流体力学：长时间稳定性和涡流不稳定性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-01-01 Epub Date: 2025-09-03 DOI: 10.1016/j.na.2025.113937

Niklas Knobel

This article considers the ideal 2D magnetohydrodynamic equations in a infinite periodic channel close to a combination of an affine shear flow, called Couette flow, and a constant magnetic field. This incorporates important physical effects, including mixing and coupling of velocity and magnetic field. We establish the existence and stability of the velocity and magnetic field for Gevrey-class perturbations of size

ɛ

, valid up to times

t \sim ɛ^{- 1}

. Additionally, the vorticity and current grow as

O (t)

and there is no inviscid damping of the velocity and magnetic field. This is similar to the above threshold case for the

3 D

Navier–Stokes (Jacob Bedrossian et al., 2022) where growth in ‘streaks’ leads to time scales of

t \sim ɛ^{- 1}

. In particular, for the ideal MHD equations, our article suggests that for a wide range of initial data, the scenario “induction by shear

\Rightarrow

vorticity and current growth

\Rightarrow

vorticity and current breakdown” leads to instability and possible turbulences.

本文考虑了无限周期通道中的理想二维磁流体动力学方程，该通道接近仿射剪切流（称为Couette流）和恒定磁场的组合。这包含了重要的物理效应，包括速度和磁场的混合和耦合。我们建立了大小为i的gevrey类扰动的速度和磁场的存在性和稳定性，有效到t ~ i−1次。此外，涡度和电流以O(t)增长，并且速度和磁场没有无粘阻尼。这类似于上述三维Navier-Stokes的阈值情况（Jacob Bedrossian et al., 2022），其中“条纹”的增长导致时间尺度为t ~ ε−1。特别是，对于理想的MHD方程，我们的文章表明，对于大范围的初始数据，“剪切诱导⇒涡度和电流增长⇒涡度和电流击穿”的情况会导致不稳定和可能的湍流。

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引用次数: 0

Fefferman–Stein type decomposition of CMO spaces in the Dunkl setting and an application Dunkl环境下CMO空间的Fefferman-Stein型分解及其应用

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications

Pub Date : 2026-01-01 Epub Date: 2025-08-14 DOI: 10.1016/j.na.2025.113916

Qingdong Guo , Ji Li , Brett D. Wick

In this paper, we establish the Fefferman–Stein type decomposition of the

CMO

space in the Dunkl setting. That is

f \in CMO (R^{d}, d ω)

if and only if

f = f_{0} + \sum_{j = 1}^{d} {\tilde{R}}_{j} f_{j},

where

f_{0}, f_{1}, \dots, f_{d} \in C_{0} (R^{d})

and

{\tilde{R}}_{j}

j = 0, 1, \dots, d

, represent the Dunkl–Riesz transforms. Our main tool is to characterize

CMO (R^{d}, d ω)

via two approximations, which are new even for the classical space

CMO (R^{d})

. As a direct application of our characterization of

CMO (R^{d}, d ω)

, we prove the duality of

CMO (R^{d}, d ω)

with

H^{1} (R^{d}, d ω)

本文建立了Dunkl环境下CMO空间的Fefferman-Stein型分解。即f∈CMO（Rd,d）当且仅当f=f0+∑j=1dR ~ jfj，其中f0，f1，…，fd∈C0（Rd）和R ~ j， j=0,1，…，d表示Dunkl-Riesz变换。我们的主要工具是通过两个近似来表征CMO(Rd,d)，这对于经典空间CMO（Rd）来说是新的。作为CMO（Rd,dω）表征的直接应用，我们证明了CMO（Rd,dω）与H1（Rd,dω）的对偶性。

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