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.


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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