摘要

This paper is concerned with the following Schrodinger equation: @@@ {-Delta u + V(x)u = f(x, u), for x is an element of R-N, u(x) -> 0, as vertical bar x vertical bar -> infinity, @@@ where the potential V and f are periodic with respect to x and 0 is a boundary point of the spectrum sigma(-Delta + V). By a new technique for showing the boundedness of Cerami sequences, we are able to obtain the existence of nontrivial solutions with mild assumptions on f.