Multiple solutions for a class of nonlinear Schrodinger equations

In this paper, we find new conditions to ensure the existence of infinitely many homoclinic type solutions for the Schrodinger equation -Deltau + V(x)u = g(x, u) for x is an element of R-N. Assuming V(x) and g(x, it) depend periodically on x, we deal with the situations where g(x, u) is, as \u\ --> infinity, asymptotically linear, or superlinear with certain hypothesis different from ones used in previous related study. Our approach is variational and we use the Cerami condition instead of the Palais-Smale one for deformation arguments. (C) 2004 Elsevier Inc. All rights reserved.