## Differential and Integral Equations

### Standing waves for a system of nonlinear Schrödinger equations in $\mathbb{R}^N$

Elisandra Gloss

#### Abstract

We study existence and concentration of positive solutions for systems of the form $-\epsilon^2\Delta u + V(x)u = \nabla F(u)$ in $\mathbb{R}^N$ where $\epsilon \gt 0$ is a small parameter, $F : [0,\infty)^k \rightarrow \mathbb{R}$ is a $C_{loc}^{1,\alpha}$ function, $N \geq 3, k \geq 1$, and the potential $V$ has a positive infimum and a well.

#### Article information

Source
Differential Integral Equations, Volume 24, Number 3/4 (2011), 281-306.

Dates
First available in Project Euclid: 25 September 2014

Gloss, Elisandra. Standing waves for a system of nonlinear Schrödinger equations in $\mathbb{R}^N$. Differential Integral Equations 24 (2011), no. 3/4, 281--306. https://projecteuclid.org/euclid.die/1411664733