# Nonradial symmetric bound states for a system of coupled Schrödinger equations

### Juncheng Wei

University of British Columbia, Vancouver, Canada### Tobias Weth

Universität Giessen, Germany

## Abstract

We consider bound state solutions of the coupled elliptic system

$Δu−u+u_{3}+βv_{2}u=0inR_{N},$

$Δv−v+v_{3}+βu_{2}v=0inR_{N},$

$u>0,v>0,u,v∈H_{1}(R_{N}),$

where $N=2,3$. It is known ([13]) that when $β<0$, there are no ground states, i.e., no least energy solutions. We show that, for certain finite subgroups of $O(N)$ acting on $H_{1}(R_{N})$, least energy solutions can be found within the associated subspaces of symmetric functions. For $β≤−1$ these solutions are nonradial. From this we deduce, for every $β≤−1$, the existence of infinitely many nonradial bound states of the system.

## Cite this article

Juncheng Wei, Tobias Weth, Nonradial symmetric bound states for a system of coupled Schrödinger equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), no. 3, pp. 279–294

DOI 10.4171/RLM/495