Existence and multiplicity results for a coupled system of Kirchhoff type equations

Abstract

This paper deals with a coupled system of Kirchhoff type equations in ${\mathbb{R}}^{3}$. Under suitable assumptions on the potential functions $V(x)$ and $W(x)$, we obtain the existence and multiplicity of nontrivial solutions when the parameter $\lambda$ is sufficiently large. The method combines the Nehari manifold and the mountain-pass theorem