Existence of multiple solutions of Kirchhoff type equation with sign-changing potential

Abstract

In this paper, we study the existence of infinitely many nontrivial solutions for a class of nonlinear Schrödinger–Kirchhoff type equation-a+b∫RN|∇u|2dxΔu+V(x)u=f(x,u)inRN,u(x)→0,as|x|→∞,where constants a>0,b>0 and the potential V(x) is allowed to be sign-changing. Under general superlinear assumption on nonlinearity f(x,u), we establish the existence of infinitely many solutions via variational methods, which unifies and improves the recent results of Wu (2011) [9].