Semilinear hemivariational inequalities at resonance
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In this paper we examine a semilinear hemivariational inequality at resonance in the first eigenvalue λ1 of (−Δ,H 0 1 (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.
Key words and phrasesHemivariational inequality at resonance locally Lipschitz functional Clarke subdifferential eigenvalue eigenfunction nonsmooth Palais-Smale condition coercive function anticoercive function mountain pass theorem saddle point theorem critical point
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