Some existence results for a periodic problem with non-smooth potential Original Research Article

In this paper, two existence results for a class of second order periodic boundary value problems with non-smooth potential are obtained. We extend the Castro–Lazer–Thews reduction method to non-smooth functionals, the obtained result is then exploited to prove the existence of a nontrivial solution. Furthermore, we prove the existence of multiple solutions by using a multiplicity result based on local linking.