We study the stability of standing waves eiωtφω(x) for a nonlinear Schrödinger equation with critical power nonlinearity |u|4/nu and a potential V (x) in Rn. Here, ω ∈ R and φω(x) is a ground state of the stationary problem. Under suitable assumptions on V (x), we show that eiωtφω(x) is stable for sufficiently large ω. This result gives a different phenomenon from the case V (x) = 0 where the strong instability was proved by M. I. Weinstein .
|Number of pages||18|
|Journal||Advances in Differential Equations|
|Publication status||Published - 2005 Dec 1|
ASJC Scopus subject areas
- Applied Mathematics