Abstract The goal of this paper is to discuss the well-posedness and the generalized well-posedness of a new kind of differential quasi-variational-hemivariational inequality (DQHVI) in Hilbert spaces. Employing these concepts, we explore the essential relation between metric characterizations and the well-posedness of DQHVI. Moreover, the compactness of the set of solutions for DQHVI is delivered, when problem DQHVI is well-posed in the generalized sense.

中文翻译：

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关于微分拟变分半变分不等式的适定性

摘要 本文的目的是讨论希尔伯特空间中一类新的微分拟变分半变分不等式（DQHVI）的适定性和广义适定性。利用这些概念，我们探索了度量特征与 DQHVI 适定性之间的基本关系。此外，当问题 DQHVI 在广义意义上是适定的时，DQHVI 的解决方案集的紧凑性就会被传递。