Ground state sign-changing solutions for the Schrödinger–Kirchhoff equation in [formula omitted]

Abstract

In this paper, with the help of variational methods in association with the deformation lemma and Miranda's theorem, we investigate the existence of a least energy sign-changing solution which has precisely two nodal domains for the following Schrödinger–Kirchhoff equation in R3:{−(a+b∫R3|∇u|2dx)Δu+V(x)u=f(u)in R3,u∈H1(R3), where a,b>0 and the potential V:R3→R+ is locally Hölder continuous and not necessarily radially symmetric.