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 Eigenvalue problems for hemivariational inequalities
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/5262

title: Eigenvalue problems for hemivariational inequalities
authors: Papageorgiou, Nikolaos
Santos, Sandrina Rafaela Andrade
Staicu, Vasile
keywords: Locally Lipschitz function
Generalized subdifferential
Linking set
AR-condition
Multiple solutions
issue date: 2008
publisher: Springer Verlag
abstract: We consider a semilinear eigenvalue problem with a nonsmooth potential (hemivariational inequality). Using a nonsmooth analog of the local Ambrosetti–Rabinowitz condition (AR-condition), we show that the problem has a nontrivial smooth solution. In the scalar case, we show that we can relax the local AR-condition. Finally, for the resonant λ = λ 1 problem, using the nonsmooth version of the local linking theorem, we show that the problem has at least two nontrivial solutions. Our approach is variational, using minimax methods from the nonsmooth critical point theory.
URI: http://hdl.handle.net/10773/5262
ISSN: 0927-6947
source: Set-Valued Analysis
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