Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 31, pp. 1-13.

Title: Nodal solutions for nonlinear Schrodinger systems

Authors: Xue Zhou (Yunnan Normal Univ., Kunming, China)
         Xiangqing Liu (Yunnan Normal Univ., Kunming, China)

Abstract: 
In this article we consider the nonlinear Schr\"odinger 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.