Existence of solutions for a class of Kirchhoff-type equations with indefinite potential

In this paper, we consider the existence of solutions of the following Kirchhoff-type problem \[ \{ {array} [c]{ll} -(a+b∫R^3|∇ u|^2dx)Δ u+ V(x)u=f(x,u),~{in}~ R³,\\ u∈ H^1(R^3), {array} . \] where $a,b$ are postive constants, and the potential $V(x)$ is continuous and indefinite in sign. Under some suitable assumptions on $V(x)$ and f, we obtain the existence of solutions by the Symmetric Mountain Pass Theorem.