Instability of standing waves of the Schrödinger equation with inhomogeneous nonlinearity

Abstract

This paper is concerned with the inhomogeneous nonlinear Shrödinger equation (INLS-equation)iu_t + Δu + V(Єx)│u│^pu = 0, x Є R^N. In the critical and supercritical cases p ≥ 4/N, with N ≥ 2, it is shown here that standing-wave solutions of (INLS-equation) on H^1(R^N) perturbation are nonlinearly unstable or unstable by blow-up under certain conditions on the potential term V with a small Є > 0