Advances in Differential Equations

Stability of standing waves for nonlinear Schrödinger equations with critical power nonlinearity and potentials

Reika Fukuizumi

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We study the stability of standing waves $e^{i \omega t}\phi_{\omega}(x)$ for a nonlinear Schrödinger equation with critical power nonlinearity $|u|^{4/n}u$ and a potential $V(x)$ in $\mathbb R^n$. Here, $\omega\in \mathbb R$ and $\phi_{\omega}(x)$ is a ground state of the stationary problem. Under suitable assumptions on $V(x)$, we show that $e^{i \omega t}\phi_{\omega}(x)$ is stable for sufficiently large $\omega$. This result gives a different phenomenon from the case $V(x)\equiv 0$ where the strong instability was proved by M.I. Weinstein [25].

Article information

Source
Adv. Differential Equations Volume 10, Number 3 (2005), 259-276.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867879

Mathematical Reviews number (MathSciNet)
MR2123132

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B35: Stability

Citation

Fukuizumi, Reika. Stability of standing waves for nonlinear Schrödinger equations with critical power nonlinearity and potentials. Adv. Differential Equations 10 (2005), no. 3, 259--276. https://projecteuclid.org/euclid.ade/1355867879.


Export citation