Ground state solutions for periodic Discrete nonlinear Schrodinger equations

In this paper, we consider the following periodic discrete nonlinear Schrodinger equation Lu-n - omega u(n) = g(n)(u(n)), n = (n(1), n(2), ..., n(m)) E Z(m), where omega is not an element of sigma(L)(the spectrum of L) and g(n)(s) is super or asymptotically linear as vertical bar s vertical bar -> infinity. Under weaker conditions on g(n), the existence of ground state solitons is proved via the generalized linking theorem developed by Li and Szulkin and concentration-compactness principle. Our result sharply extends and improves some existing ones in the literature.