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

Abstract: In this paper, we consider the existence of solutions of the following Kirchhoff-type problem \[
\left\{
\begin{array}
[c]{ll}
-\left(a+b\int_{\mathbb{R}^3}|\nabla u|^2dx\right)\Delta u+ V(x)u=f(x,u),~{\rm{in}}~ \mathbb{R}^{3},\\
u\in H^1(\mathbb{R}^3),
\end{array} \right. \] 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.