On the standing wave for a class of nonlinear Schrödinger equations

This paper is concerned with the standing wave for a class of nonlinear Schrödinger equations iϕt + ϕ − |x|2ϕ +μ|ϕ|p−1ϕ + γ |ϕ|q−1ϕ = 0, which describes the attractive Bose–Einstein condensates under a magnetic trap. We establish the existence of the standing wave of the equation. Furthermore, we prove that the standing wave is nonlinearly unstable. © 2007 Elsevier Inc. All rights reserved.