M. E. Filippakis, N. S. Papageorgiou
Department of Mathematics, School of Applied Mathematics and Natural Science, National Technical University, Zografou Campus, Athena 15780, Greece
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.
Keywords.Locally Lipschitz function, generalized subdifferential, $p$-Laplacian, homogeneous function, variational method, Poincare-Wirtinger inequality, potential indefinite in sign.