M. E. Filippakis, N. S. Papageorgiou
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, npapg@math.ntua.gr
Abstract.
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.