A class of variational-hemivariational inequalities of elliptic type. (English) Zbl 1196.35111

Liu, Zhenhai; Motreanu, Dumitru

Nonlinearity 23, No. 7, 1741-1752 (2010).

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.

MSC:

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

Keywords:

variational methods for elliptic systems; variational methods including variational inequalities