Equilibrium problems with trifunctions and applications to hemivariational inequalities

Abstract

In this paper, we define generalized monotonicity concepts related to equilibrium problems generated by trifunctions. We then study the existence of solutions to mixed equilibrium problems described as the sum of a maximal monotone trifunction and a pseudomonotone trifunction in Brézis sense. The main tools for this study are a Thikonov regularization procedure with respect to the generalized duality mapping and recession analysis adapted to trifunctions. An application consists in an existence result for a noncoercive hemivariational inequality.