Existence and asymptotic behavior of positive ground state solutions for nonlinear Kirchhoff problems

Abstract

We consider the existence of positive ground state solutions to the following equation−(a+b∫R3|∇u|2)Δu+Vϵ(x)u=bγ(x)|u|pu,u∈H1(R3),under some assumptions on Vϵ(x) and bγ(x), where p ∈ (2, 4) and a, b > 0. Moreover, we also study asymptotic behavior of the solutions obtained above as (ϵ, γ) tends to some fixed point.