Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in R3R3

In this paper, we study the following nonlinear problem of Kirchhoff type with pure power nonlinearities:equation(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>0a,b>0 are constants, 20,x∈R3, where ε>0ε>0 is a parameter, V(x)V(x) is a positive continuous potential and f(u)∼|u|p−1uf(u)∼|u|p−1u with 3