Department of Mathematics
Yunnan Normal University
Kunming 650221, China
email: niuzhoux@163.com
Department of Mathematics
Yunnan Normal University
Kunming 650221, China
email: lxq8u8@163.com
Xue Zhou, Xiangqing Liu
Abstract:
In this article we consider the nonlinear Schrodinger system
$$\displaylines{
- \Delta u_j + \lambda_j u_j = \sum_{i=1}^k \beta_{ij} u_i^2 u_j, \quad \hbox{in } \Omega, \cr
u_j ( x ) = 0,\quad \hbox{on } \partial \Omega , \; j=1,\ldots,k ,
}$$
where \(\Omega\subset \mathbb{R}^N \) (\(N=2,3 \)) is a bounded smooth domain,
\(\lambda_j> 0\), \(j=1,\dots,k\), \( \beta_{ij} \) are constants satisfying \(\beta_{jj}>0\),
\(\beta_{ij}=\beta_{ji}\leq0 \) 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.
Submitted December 9, 2023. Published April 24, 2024.
Math Subject Classifications: 35A15, 35B20, 35J10.
Key Words: Schrodinger system; sign-changing solutions; truncation method; method of invariant sets of descending flow.
DOI: 10.58997/ejde.2024.31
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| Xue Zhou Department of Mathematics Yunnan Normal University Kunming 650221, China email: niuzhoux@163.com | |
|
Xiangqing Liu Department of Mathematics Yunnan Normal University Kunming 650221, China email: lxq8u8@163.com |
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