### An existence and stability result for standing waves of nonlinear Schrödinger equations

#### Abstract

We consider a nonlinear Schrödinger equation with a nonlinearity of the form $V(x)g(u)$. Assuming that $V(x)$ behaves like $|x|^{-b}$ at infinity and $g(s)$ like $|s|^p$ around $0$, we prove the existence and orbital stability of travelling waves if $1 < p < 1+(4-2b)/N$.

#### Article information

Source
Adv. Differential Equations Volume 11, Number 7 (2006), 813-840.

Dates
First available in Project Euclid: 18 December 2012