## Advances in Differential Equations

### 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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867677

Mathematical Reviews number (MathSciNet)
MR2236583

Zentralblatt MATH identifier
1155.35095

#### Citation

Jeanjean, Louis; Le Coz, Stefan. An existence and stability result for standing waves of nonlinear Schrödinger equations. Adv. Differential Equations 11 (2006), no. 7, 813--840. https://projecteuclid.org/euclid.ade/1355867677