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Existence results for quasilinear hemivariational inequalities at resonance

Pages: 409 - 418, Issue Special, September 2007

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Leszek Gasiński - Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30072 Kraków, Poland (email)

Abstract: In this paper we consider quasilinear hemivariational inequality at resonance. We obtain two existence theorems using a Landesman-Lazer type condition. The method of the proof is based on the nonsmooth critical point theory for locally Lipschitz functions.

Keywords:  p-Laplacian, strong resonance at infinity, first eigenvalue,Clarke subdifferential, nonsmooth Palais-Smile condition, nonsmooth Cerami condition, Landesman-Lazer type conditions, mountain pass theorem.
Mathematics Subject Classification:  Primary: 49J40; Secondary: 34B15, 35J20.

Received: July 2006;      Revised: May 2007;      Published: September 2007.