Existence results for quasilinear parabolic hemivariational inequalities

Abstract: This paper is devoted to the periodic problem for quasilinear parabolic hemivariational inequalities at resonance as well as at nonresonance. By use of the theory of multi-valued pseudomonotone operators, the notion of generalized gradient of Clarke and the property of the first eigenfunction, we build a Landesman–Lazer theory in the nonsmooth framework of quasilinear parabolic hemivariational inequalities. [Copyright &y& Elsevier]