A nonlinear periodic system with nonsmooth potential of indefinite sign

M. E. Filippakis, N. S. Papageorgiou

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

E-mail.   mfilip@math.ntua.gr, npapg@math.ntua.gr

In this paper we consider a nonlinear periodic system driven bythe vector ordinary $p$-Laplacian and having a nonsmooth locally Lipschitz potential, which is positively homogeneous. Using a variational approach which exploits the homogeneity of the potential, we establish the existence of a nonconstant solution.

AMSclassification. 34C25.

Keywords.Locally Lipschitz function, generalized subdifferential, $p$-Laplacian, homogeneous function, variational method, Poincare-Wirtinger inequality, potential indefinite in sign.