In this paper we study a new abstract evolutionary variational–hemivariational inequality which involves unilateral constraints and history–dependent operators. First, we prove the existence and uniqueness of solution by using a mixed equilibrium formulation with suitable selected functions together with a fixed-point principle for history–dependent operators. Then, we apply the abstract result to show the unique weak solvability to a dynamic viscoelastic frictional contact problem. The contact law involves a unilateral Signorini-type condition for the normal velocity combined with 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.

在本文中，我们研究了一个新的抽象演化变分-半变异不等式，它涉及单边约束和历史相关算子。首先，我们通过使用混合平衡制剂与合适的选择的功能一起与历史相关的运营商的固定点原则证明的溶液存在唯一性。然后，我们将抽象结果应用于显示动态粘弹性摩擦接触问题的独特弱可溶性。接触定律涉及法向速度的单边Signorini型条件和非单调的正常阻尼响应条件，而摩擦条件是干摩擦库仑定律的一种形式，其中摩擦范围取决于累积的滑移。