We consider a new class of inclusions in Hilbert spaces for which we provide an existence and uniqueness result. The proof is based on arguments of monotonicity, convexity and fixed point. We use this result to establish the unique solvability of an associated class of Moreau’s sweeping processes. Next, we give two applications in Solid Mechanics. The first one concerns the study of a time-dependent constitutive law with unilateral constraints and memory term. The second one is related to a frictional contact problem for viscoelastic materials. For both problems we describe the physical setting, list the assumptions on the data and provide existence and uniqueness results.

我们考虑希尔伯特空间中的一类新的包含物，为此我们提供了一个存在性和唯一性结果。该证明基于单调性，凸性和不动点的论点。我们使用此结果来建立Moreau扫掠过程的相关类的独特可解性。接下来，我们在固体力学中给出两个应用程序。第一个涉及单边约束和记忆项的时变本构法的研究。第二个问题涉及粘弹性材料的摩擦接触问题。对于这两个问题，我们都将描述物理环境，列出数据假设并提供存在性和唯一性结果。