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In this paper we consider an abstract class of time-dependent quasi variational-hemivariational inequalities which involves history-dependent operators and a set of unilateral constraints. First, we establish the existence and uniqueness of solution by using a recent result for elliptic variational-hemivariational inequalities in reflexive Banach spaces combined with a fixed-point principle for history-dependent operators. Then, we apply the abstract result to show the unique weak solvability to a quasistatic viscoelastic frictional contact problem. The contact law involves a unilateral Signorini-type condition for the normal velocity and the nonmonotone normal damped response condition while the friction condition is a version of the Coulomb law of dry friction in which the friction bound depends on the accumulated slip., Comment: 15p

The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We establish the nonemptiness and compactness of the solution set to the system. We apply a new method of proof based on a multivalued version of the Tychonoff fixed point principle in a Banach space combined with the generalized monotonicity arguments, and elements of the nonsmooth analysis. Our results improve and generalize some earlier theorems obtained for a very particular form of the system., Comment: 17p