In the present paper, we focus on a class of multivalued variational–hemivariational inequalities with pseudomonotone operator and constraint set in Hilbert spaces. By employing the penalty method and the Moreau–Yosida approximation technique, we construct an approximating problem for the original multivalued variational–hemivariational inequality under consideration. The main result in the paper shows that every weak cluster of the solution sequence for the approximating problem is always a solution of the original problem. Moreover, based on the obtained weak convergence result, another two strong convergence results are obtained when the condition of pseudomonotonicity is reinforced. Finally, we illustrate the application of our abstract results in the study of a frictionless contact problem in mechanics with unilateral constraint.

在本文中，我们关注一类在希尔伯特空间中具有伪单调算子和约束集的多值变分-半变分不等式。通过采用惩罚方法和 Moreau-Yosida 逼近技术，我们为所考虑的原始多值变分-半变分不等式构造了一个逼近问题。论文中的主要结果表明，逼近问题的解序列的每个弱聚类总是原问题的解。此外，根据得到的弱收敛结果，在增强伪单调性条件的情况下，得到另外两个强收敛结果。最后，我们说明了我们的抽象结果在单边约束力学中的无摩擦接触问题研究中的应用。