On the Existence of Solutions for a Class of Schrödinger–Kirchhoff-Type Equations with Sign-Changing Potential

Abstract

In this paper, we consider the following Kirchhoff problem − a + b ∫ R 3 ∇ u 2 d x Δ u + λ V x u = u p − 2 u , in R 3 u ∈ H 1 R 3 where a , b > 0 are constants, λ is a positive parameter, and 4 < p < 6 . Under suitable assumptions on V x , the existence of nontrivial solution is obtained via variational methods. The potential V x is allowed to be sign-changing.