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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019047

Mathematical Reviews number (MathSciNet)
MR2759354

Zentralblatt MATH identifier
1240.35199

Citation

Carvalho, Janete S.; Maia, Liliane A.; Miyagaki, Olimpio H. Antisymmetric solutions for the nonlinear Schrödinger equation. Differential Integral Equations 24 (2011), no. 1/2, 109--134. https://projecteuclid.org/euclid.die/1356019047