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

In this paper, we study the following Schrödinger–Kirchhoff-type problem: [Formula: see text], [Formula: see text], where a > 0 and b > 0 are small enough. Under suitable assumptions on f, we obtain the existence of ground state sign-changing solution u b 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.