On a Schrodinger equation with periodic potential and spectrum point zero

In this paper, we study a nonlinear Schrodinger equation with periodic potential. We assume that zero is an end point of the continuous spectrum of the Schrodinger operator. We establish some existence results of the homoclinic orbits for weak superlinear cases. To this purpose, we develop new linking theorems in Banach Spaces which provide bounded Palais-Smale sequences.