We study a nonlinear elliptic differential inclusion involving monotone and nonmonotone terms. Our formulation incorporates variational-hemivariational inequalities. The problem is strongly nonlinear in the sense that on the nonmonotone multivalued term we do not impose any growth condition and instead we use a generalized sign condition. Our approach is based on methods and techniques from multivalued analysis and from the theory of nonlinear operators of monotone type.
"Existence of solutions for strongly nonlinear elliptic differential inclusions with unilateral constraints." Adv. Differential Equations 10 (9) 961 - 982, 2005.