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.


35J87 Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators
49J40 Variational inequalities
35P05 General topics in linear spectral theory for PDEs
65N20 Numerical methods for ill-posed problems for boundary value problems involving PDEs
35B34 Resonance in context of PDEs
47N20 Applications of operator theory to differential and integral equations
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