Periodic solutions for systems with nonsmooth and partially coercive potential

M. E. Filippakis

Department of Mathematics, School of Applied Mathematics and Natural Science, National Technical University, Zografou Campus, Athena 15780, Greece


In this paper we consider nonlinear periodic systems driven by the one-dimensional $p$-Laplacian and having a  non smooth locally Lipschitz potential. Using a variational approach based on the nonsmooth Critical Point Theory, we establish the existence of a solution. We also prove a multiplicity result based on a nonsmooth extension of the result of Brezis-Nirenberg [3] due to Kandilakis-Kourogenis-Papageorgiou [13].

AMSclassification. 34A60.

Keywords.   Locally linking Lipschitz function, generalized subdifferential, nonsmooth critical point theory, nonsmooth Palais-Smale condition, $p$-Laplacian, periodic system.