Nodal solutions for nonlinear Schrodinger systems

IF 0.8 4区数学 Q2 MATHEMATICS

Electronic Journal of Differential Equations Pub Date : 2024-04-24 DOI:10.58997/ejde.2024.31

Xue Zhou, Xiangqing Liu

引用次数: 0

Abstract

In this article we consider the nonlinear Schrodinger system $$\displaylines{ - \Delta u_j + \lambda_j u_j = \sum_{i=1}^k \beta_{ij} u_i^2 u_j, \quad \hbox{in } \Omega, \cr u_j ( x ) = 0,\quad \hbox{on } \partial \Omega , \; j=1,l\dots,k , }$$ where $\Omega\subset \mathbb{R}^N $ ($N=2,3$) is a bounded smooth domain, $\lambda_j> 0$, $j=1,\ldots,k$, $\beta_{ij}$ are constants satisfying $\beta_{jj}>0$, $\beta_{ij}=\beta_{ji}\leq 0 $ for $1\leq i< j\leq k$. The existence of sign-changing solutions is proved by the truncation method and the invariant sets of descending flow method. For more information see https://ejde.math.txstate.edu/Volumes/2024/31/abstr.html

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非线性薛定谔系统的节点解

在本文中，我们考虑了非线性薛定谔系统 $$\displaylines{ - \Delta u_j + \lambda_j u_j = \sum_{i=1}^k \beta_{ij} u_i^2 u_j, \quad \hbox{in }\Omega, \cr u_j ( x ) = 0,\quad \hbox{on }.\Omega, \cr u_j ( x ) = 0,\quad \hbox{on }\partial \Omega ,\；j=1,l\dots,k , }$$ 其中 $\Omega\subset \mathbb{R}^N $ ($N=2,3$) 是一个有界的光滑域, $\lambda_j> 0$, $j=1、\(beta_{jj}>0),（beta_{ij}=beta_{ji}/leq 0$ for$1\leq i< j\leq k$.符号变化解的存在性是通过截断法和降流不变集法证明的。更多信息见 https://ejde.math.txstate.edu/Volumes/2024/31/abstr.html

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

Electronic Journal of Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

3 months

期刊介绍： All topics on differential equations and their applications (ODEs, PDEs, integral equations, delay equations, functional differential equations, etc.) will be considered for publication in Electronic Journal of Differential Equations.