Ground state sign-changing solutions for Schrödinger–Kirchhoff-type problem with critical growth

Abstract

In this paper, we study the following Schrödinger–Kirchhoff-type problem: −a+b∫R3|∇u|2dx△u+u=|u|4u+f(u), x∈R3, where a > 0 and b > 0 are small enough. Under suitable assumptions on f, we obtain the existence of ground state sign-changing solution ub by the constraint variational method with Miranda’s theorem. Moreover, we prove that its energy is strictly larger than twice that of the ground state solution.