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Ground state solutions for the nonlinear Kirchhoff type equations with lower term

In this paper, we consider the following nonlinear Kirchhoff type equations: −a+b∫R3|∇u|2Δu+λV(x)u=|u|p−2u in R3, where a, b > 0, λ ≥ 1, V∈C(R3,R) is a potential well and 3 < p < 6. Under suitable assumptions on V, the existence and concentrating behavior of solutions to a problem are obtained by using variational methods. We mainly extend the results about nonlinear Kirchhoff type equations with potential by Li and Ye [J. Differ. Equations 257(2), 566–600 (2014)] to the Kirchhoff type equations with sign-changing potential well.