(1) Institute of Computer Science, Jagiellonian University, ul. Nawojki 11, 30072 Cracow, Poland;(2) Department of Mathematics, National Technical University, Zografou Campus, 15780 Athens, Greece
Abstract:
In this paper we examine a semilinear hemivariational inequality at resonance in the first eigenvalue λ1 of (−Δ,H01
(Z)). We prove two existence theorems for such problems. Our approach is variational and is based on the nonsmooth critical
point theory of Chang, which uses the subdifferential calculus of Clarke for locally Lipschitz functions.