|Existence and Multiplicity Results for Quasilinear Hemivariational Inequalities at Resonance|
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
Abstract: In this paper we consider quasilinear hemivariational inequality at resonance. We obtain two existence theorems using a Landesman-Lazer type condition and an Ambrosetti-Rabinowitz type condition as well as two multiplicity results. The method of the proofs is based on the nonsmooth critical point theory for locally Lipschitz functions.
Keywords: p-Laplacian, strong resonance at infinity, first eigenvalue, Clarke subdifferential, nonsmooth Cerami condition, Landesman-Lazer type condition, Ambrosetti-Rabinowitz type condition, mountain pass theorem.
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