## Differential and Integral Equations

### Antisymmetric solutions for the nonlinear Schrödinger equation

#### Abstract

In this article, we consider the nonlinear Schrödinger equation $$-\Delta u + V(x)u=|u|^{p-1}u \quad \text{in} \quad \mathbb{R}^N.$$ Here $V$ is invariant under an orthogonal involution. The basic tool employed here is the concentration--compactness principle. A theorem on existence of a solution which changes sign exactly once is given.

#### Article information

Source
Differential Integral Equations, Volume 24, Number 1/2 (2011), 109-134.

Dates
First available in Project Euclid: 20 December 2012