In this paper, we deal with a class of second-order evolutionary history-dependent variational–hemivariational inequalities with constraint. The unique solvability of the considered second-order evolutionary inequality problem is established via a surjectivity result combined with a fixed point theorem. Moreover, we construct a regularized problem for such second-order evolutionary history-dependent variational–hemivariational inequality and show the convergence of the regularized solutions toward the solution of the original problem under some mild assumptions.

中文翻译：

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一类广义二阶演化变分-半变分不等式的收敛结果

在本文中，我们处理一类具有约束的二阶进化历史相关变分-半变分不等式。所考虑的二阶演化不等式问题的唯一可解性是通过满射结果与不动点定理相结合建立的。此外，我们为这种二阶演化历史依赖的变分半变分不等式构造了一个正则化问题，并在一些温和的假设下证明了正则化解向原始问题解的收敛性。