Ground state solutions and least energy sign-changing solutions for a class of fourth order Kirchhoff-type equations in [formula omitted

Abstract

In this article we study the problem Δ2u−(1+λ∫RN|∇u|2dx)Δu+V(x)u=|u|p−2uin RN, where Δ2≔Δ(Δ) is the biharmonic operator, λ>0 is a parameter, p∈(2,2∗), and V(x)∈C(RN,R). Under appropriate assumptions on V(x), the existence of ground state solutions and a least energy sign-changing solution is obtained by combining the variational methods and the Nehari method.