Orbital stability of standing waves for a class of Schrödinger equations with unbounded potential

Chen, Guanggan; Zhang, Jian; Wei, Yunyun

doi:https://doi.org/10.1155/JAMSA/2006/57676

International Journal of Stochastic Analysis

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Volume 2006 | Article ID 057676 | https://doi.org/10.1155/JAMSA/2006/57676

Orbital stability of standing waves for a class of Schrödinger equations with unbounded potential

Guanggan Chen,¹Jian Zhang,²and Yunyun Wei³

Received26 Aug 2004

Revised20 Oct 2004

Accepted09 Nov 2004

Published03 Jan 2006

Abstract

This paper is concerned with the nonlinear Schrödinger equation with an unbounded potential iϕt=−Δϕ+V(x)ϕ−μ|ϕ|p−1ϕ−λ|ϕ|q−1ϕ, x∈ℝN, t≥0, where μ>0, λ>0, and 1<p<q<1+4/N. The potential V(x) is bounded from below and satisfies V(x)→∞ as |x|→∞. From variational calculus and a compactness lemma, the existence of standing waves and their orbital stability are obtained.

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Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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