Solutions and multiple solutions for periodic p-Laplacian systems with a non-smooth potential

Abstract

In this article, we study non-linear periodic systems driven by the ordinary vector p-Laplacian differential operator and with a non-smooth potential. Using variational methods based on the non-smooth critical point theory, we prove an existence and a multiplicity theorems. The conditions on the non-smooth potential do not imply that the corresponding Euler functional of the problem is coercive.

Keywords:

• vector p-Laplacian
• non-smooth potential
• generalized subdifferential
• non-smooth second deformation theorem
• non-smooth PS-condition
• locally Lipschitz functional

AMS Subject Classification::

• 34C25

Acknowledgement

This paper has been partially supported by the State Committee for Scientific Research of Poland (KBN) under research grant no. N201 027 32/1449.