Infinitely many solutions for a Schrodinger equation with sign-changing potential and nonlinear term

We propose a new variational approach to finding multiple critical points for strongly indefinite problems without assuming the weak upper semicontinuity on the variational functionals. By this approach, we obtain the existence of infinitely many geometrically distinct solutions for a stationary periodic Schr"odinger equation, in which the linear part is strongly indefinite and the nonlinear term is allowed to change sign in general ways.