  We study the Schr\"{o}dinger equation: \begin{eqnarray} - \Delta
u+V(x)u+f(x,u)=0,\qquad u\in H^{1}(\mathbb{R}^{N}),\nonumber \end{eqnarray}
where $V$ is periodic and $f$ is periodic in the $x$-variables, $0$ is in a gap
of the spectrum of the operator $-\Delta+V$. We prove that under some new
assumptions for $f$, this equation has a nontrivial solution. Our assumptions
for the nonlinearity $f$ are very weak and greatly different from the known
assumptions in the literature.
