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Periodic solutions for systems with nonsmooth and partially coercive potential

Michael E. Filippakis — 2006

Archivum Mathematicum

In this paper we consider nonlinear periodic systems driven by the one-dimensional $p$ -Laplacian and having a nonsmooth 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 (Brezis, H., Nirenberg, L., Remarks on finding critical points, Comm. Pure Appl. Math. 44 (1991), 939–963.) due to Kandilakis-Kourogenis-Papageorgiou...

Periodic solutions for differential inclusions in $ℝ^{N}$

Michael E. Filippakis; Nikolaos S. Papageorgiou — 2006

Archivum Mathematicum

We consider first order periodic differential inclusions in $ℝ^{N}$ . The presence of a subdifferential term incorporates in our framework differential variational inequalities in $ℝ^{N}$ . We establish the existence of extremal periodic solutions and we also obtain existence results for the “convex” and “nonconvex”problems.

A nonlinear periodic system with nonsmooth potential of indefinite sign

Michael E. Filippakis; Nikolaos S. Papageorgiou — 2006

Archivum Mathematicum

In this paper we consider a nonlinear periodic system driven by the 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.