In this paper, we consider the following semilinear elliptic systems: {-Δu+V(x)u=Fu(x,u,v),inRN,-Δv+V(x)v=Fv(x,u,v),inRN,where V:RN→R,Fu(x,u,v) and Fv(x, u, v) are periodic in x. We assume that 0 is a right boundary point of the essential spectrum of - ▵+ V. Under appropriate assumptions on Fu(x, u, v) and Fv(x, u, v) , we prove the above system has a ground-state solution by using the Nehari-type technique in a strongly indefinite setting. Furthermore, the existence of infinitely many geometrically distinct solutions is obtained via variat...
