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

In this paper, we investigate the existence of least energy sign-changing solutions for the Kirchhoff-type problem − a + b ∫ R 3 | ∇ u | 2 d x Δ u + V (x) u = f (u) , x ∈ R 3 , where a, b > 0 are parameters, V ∈ C ( R 3 , R) , and f ∈ C (R , R). 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. [ABSTRACT FROM AUTHOR]