New type of solutions for the nonlinear Schrödinger equation in RN

Abstract

We construct a new family of entire solutions for the nonlinear Schrödinger equation{−Δu+V(y)u=up,u>0,inRN,u∈H1(RN), where p∈(1,N+2N−2) and N≥3, and V(y)=V(|y|) is a positive bounded radial potential satisfyingV(|y|)=V0+a|y|m+O(1|y|m+σ),as|y|→∞, for some fixed constants V0,a,σ>0, and m>max⁡{4p−1,2}.

Topics & Concepts