Concentration Phenomena of Sign-Changing Solutions for the Planar Schrödinger-Poisson Systems

IF 1.7 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-07-18 DOI:10.1007/s00245-025-10289-9

Yiqing Li, Patrizia Pucci, Binlin Zhang

引用次数: 0

Abstract

This paper investigates the existence and concentration behavior of nodal solutions for the planar Schrödinger-Poisson system with subcritical exponential growth

$$\begin{aligned} \left\{ \begin{array}{l} -\Delta u+V(\varepsilon x)u+\mu \phi u= f(u)\ \ \text{ in }\ {\mathbb {R}}^2,\\ \Delta \phi =u^2\ \ \text{ in }\ {\mathbb {R}}^2, \end{array}\right. \qquad \qquad \qquad ({\mathcal {S}}) \end{aligned}$$

where $\varepsilon, \mu >0$ are parameters, V and f are continuous functions. Under suitable assumptions, the existence of nodal solutions is established, using variational methods. Furthermore, we prove that the nodal solutions of (${\mathcal {S}}$) concentrate around the minimum point of V and exhibit exponential decay at infinity.

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平面Schrödinger-Poisson系统变符号解的集中现象

本文研究了具有次临界指数增长$$\begin{aligned} \left\{ \begin{array}{l} -\Delta u+V(\varepsilon x)u+\mu \phi u= f(u)\ \ \text{ in }\ {\mathbb {R}}^2,\\ \Delta \phi =u^2\ \ \text{ in }\ {\mathbb {R}}^2, \end{array}\right. \qquad \qquad \qquad ({\mathcal {S}}) \end{aligned}$$的平面Schrödinger-Poisson系统节点解的存在性和集中性，其中$\varepsilon, \mu >0$为参数，V和f为连续函数。在适当的假设条件下，利用变分方法建立了节点解的存在性。进一步证明了（${\mathcal {S}}$）的节点解集中在V的最小点周围，并在无穷远处呈现指数衰减。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.