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Zbl 1139.35006
Liu, Zhenhai
Existence results for quasilinear parabolic hemivariational inequalities. (English)
[J] J. Differ. Equations 244, No. 6, 1395-1409 (2008). ISSN 0022-0396

In this paper it is studied a class of parabolic hemivariational inequalities involving pseudomonotone operators. The main result of the paper establishes the existence of a nontrivial solution. Connections with the Landesman-Lazer resonance theory are also made in the present paper. The proofs rely on monotonicity arguments combined with the Clarke critical point theory for locally Lipschitz functionals.
[Vicenţiu D. Rădulescu (Craiova)]

MSC 2000:: *35A15 Variational methods (PDE)
35K85 Unilateral problems; variational inequalities (parabolic type)
49J40 Variational methods including variational inequalities

Keywords: generalized Clarke subdifferential; pseudomonotone operator; Landesman-Lazer resonance theory

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