Non-degeneracy of the ground state solution on nonlinear Schrödinger equation

Abstract

We are concerned with the following nonlinear Schrödinger equation −ε2Δu+V(x)u=|u|p−2u,u∈H1(RN),where ε>0 is a small parameter, N≥1, 2<p<2∗. We prove the non-degeneracy of the ground state solution to the above problem by using local Pohozaev identity and blow-up analysis, which fills the gap in this aspect.