Nodal solutions for nonlinear Schrodinger systems

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