Infinitely many solutions for a superlinear Neumann problem in tileable regions

We establish the existence of infinitely many solutions to a super-linear Neumann problem on regions that can be tiled by regular prisms. Our proofs take advantage of recent results on the existence of sign-changing solutions for superlinear problems. The nonlinearities under consideration are not perturbations of odd nonlinearities where Liusternik-Schnirelman arguments may be applied.