Existence results for quasilinear parabolic hemivariational inequalities. (English) Zbl 1139.35006

Liu, Zhenhai

J. Differ. Equations 244, No. 6, 1395-1409 (2008).

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.

Reviewer: Vicenţiu D. Rădulescu (Craiova)

MSC:

35A15	Variational methods applied to PDEs
35K85	Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
49J40	Variational inequalities

Keywords:

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

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