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

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