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2005 Stability of standing waves for nonlinear Schrödinger equations with critical power nonlinearity and potentials
Reika Fukuizumi
Adv. Differential Equations 10(3): 259-276 (2005).

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].

Citation

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Reika Fukuizumi. "Stability of standing waves for nonlinear Schrödinger equations with critical power nonlinearity and potentials." Adv. Differential Equations 10 (3) 259 - 276, 2005.

Information

Published: 2005
First available in Project Euclid: 18 December 2012

zbMATH: 1107.35100
MathSciNet: MR2123132

Subjects:
Primary: 35Q55
Secondary: 35B35

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.10 • No. 3 • 2005
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