Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in R3

Abstract

In this paper, we study the following nonlinear problem of Kirchhoff type with pure power nonlinearities:. (0.1){-(a+b∫R3|Du|2)δu+V(x)u=|u|p-1u,x∈R3,u∈H1(R3),u>0,x∈R3, where a, b>. 0 are constants, 2. 0,x∈R3, where ε>0 is a parameter, V(x) is a positive continuous potential and f(u)~|u|p-1u with 3