Existence of Positive and of Multiple|
Solutions for Nonlinear Periodic Problems
Zdzisław Denkowski, denkowski(at)softlab.ii.uj.edu.pl
Leszek Gasiński, gasinski(at)softlab.ii.uj.edu.pl, http://www.ii.uj.edu.pl/~gasinski/
Jagiellonian University, Institute of Computer Science, Nawojki 11, 30-072 Cracow, Poland
Nikolaos S. Papageorgiou
National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece
Abstract: In this paper we consider a scalar periodic problem driven by the ordinary p-Laplacian differential operator and having a nonsmooth potential. Using a variational method based on a nonsmooth critical point theory, first we prove the existence of a strictly positive solution. Then by strengthen our hypotheses on the nonsmooth potential, we prove the existence of a second periodic solution.
Keywords: Locally Lipschitz functions, Clarke subdifferential, nonsmooth Cerami condition, generalized nonsmooth Palais-Smale condition, local minimum, nonsmooth mountain pass theorem.
epmsnpp_p051.ps (510 K), epmsnpp_p051.pdf (216 K)