On the Existence of Multiple Periodic Solutions for Equations Driven by the p-Laplacian and with a Nonsmooth Potential



L. Gasiński, gasinski(at)softlab.ii.uj.edu.pl, http://www.ii.uj.edu.pl/~gasinski/
Nikolaos S. Papageorgiou
       Jagiellonian University, Institute of Computer Science, Nawojki 11, 30-072 Cracow, Poland


Abstract: In this paper we examine periodic problems driven by the scalar p-Laplacian. Using nonsmooth critical point theory and a recent multiplicity result based on local linking (the original smooth version is due to Brezis-Nirenberg), we prove three multiplicity results, the third for semilinear problems with resonance at zero. Also we study a quasilinear periodic eigenvalue problem with the parameter near resonance. We prove the existence of three distinct solutions, extending this way a semilinear and smooth result of Mawhin-Schmitt.

Published: Proceedings of the Edinburgh Mathematical Society, 46 (2003), 229-249.