Nontrivial solutions for Kirchhoff equations with periodic potentials

In this article we consider the Kirchhoff equations $$ -\Big(a+b\int_{\mathbb{R}^3}|\nabla u|^2\Big)\Delta u+V(x)u=f(x,u),\quad x\in\mathbb{R}^3, $$ where $a,b>0$ are constants, the nonlinearity f is superlinear at infinity with subcritical or critical growth and V is positive, continuous and periodic in x. Some existence results for ground state solutions are obtained by using variational methods. Moreover, when $V\equiv 1$ we obtain ground state solutions for the above problem with a wide class of superlinear nonlinearities by using a new approach