Least energy sign-changing solutions for Kirchhoff-type problems with potential well

Abstract

In this paper, we investigate the existence of least energy sign-changing solutions for the Kirchhoff-type problem [Formula: see text], where a, b > 0 are parameters, [Formula: see text], and [Formula: see text]. Under weaker assumptions on V and f, by using variational methods with the aid of a new version of global compactness lemma, we prove that this problem has a least energy sign-changing solution with exactly two nodal domains, and its energy is strictly larger than twice that of least energy solutions.