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A class of variational-hemivariational inequalities of elliptic type. (English) Zbl 1196.35111
Summary: This paper is devoted to the existence of solutions for variational-hemivariational inequalities of elliptic type, with a higher order quasilinear principal part, at resonance as well as at nonresonance. The approach relies on the use of pseudomonotone operators. By means of the notion of Clarke’s generalized gradient and the properties of the first eigenfunction of the quasilinear principal part, we also build a Landesman-Lazer theory in the nonsmooth framework of variational-hemivariational inequalities of elliptic type.

35J87Nonlinear elliptic unilateral problems; nonlinear elliptic variational inequalities
49J40Variational methods including variational inequalities
35P05General topics in linear spectral theory of PDE
65N20Ill-posed problems (BVP of PDE, numerical methods)
35B34Resonances in solutions of PDE
47N20Applications of operator theory to differential and integral equations
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