Ground state solutions for an asymptotically linear diffusion system

This article concerns the diffusion system $$\displaylines{ \partial_tu-\Delta_{x}u+V(x)u=g(t,x,v),\cr -\partial_tv-\Delta_{x}v+V(x)v=f(t,x,u), }$$ where $z=(u,v): \mathbb{R}\times \mathbb{R}^N\to \mathbb{R}^2$, $V(x)\in C(\mathbb{R}^N,\mathbb{R})$ is a general periodic function, g, f are periodic in t, x and asymptotically linear in u, v at infinity. We find a minimizing Cerami sequence of the energy functional outside the Nehari-Pankov manifold $\mathcal{N}$ and therefore obtain ground state solutions.