Address.
Department of Mathematics, School of Applied
Mathematics and Natural Science, National Technical University, Zografou Campus, Athena 15780, Greece
E-mail. mfilip@math.ntua.gr
Abstract.
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.