  We consider standing waves with frequency $\omega$ for 4-superlinear
Schr\"odinger-Poisson system. For large $\omega$ the problem reduces to a
system of elliptic equations in $\mathsf{R}^3$ with potential indefinite in
sign. The variational functional does not satisfy the mountain pass geometry.
The nonlinearity considered here satisfies a condition which is much weaker
than the classical (AR) condition and the condition (Je) of Jeanjean. We obtain
nontrivial solution and, in case of odd nonlinearity an unbounded sequence of
solutions via the local linking theorem and the fountain theorem, respectively.
