ON THE EXISTENCE OF SOLUTIONS FOR SOME KIND OF MIXED EVOLUTIONARY VARIATIONAL-HEMIVARIATIONAL INEQUALITY PROBLEMS

This paper discusses the mixed evolutionary variational-hemivariational inequality problem, which incorporates a set of constraints and history-dependent operators. We utilized a mixed equilib- rium formulation with appropriate functions and a fixed-point principle for history-dependent operators to prove the existence and uniqueness of solutions. As an application to demonstrate the peculiar weak solution for a viscoelastic frictional contact problem that involves the unilateral signorini type condi- tion for the normal velocity together with non-monotone normal damped response conditions and the Coulomb law of dry friction that friction bounds depend on the amount of accumulated slip.