<p style='text-indent:20px;'>This paper deals with a class of history-dependent frictional contact problem with the surface traction affected by the impulsive differential equation. The weak formulation of the contact problem is a history-dependent hemivariational inequality with the impulsive differential equation. By virtue of the surjectivity of multivalued pseudomonotone operator theorem and the Rothe method, existence and uniqueness results on the abstract impulsive differential hemivariational inequalities is established. In addition, we consider the stability of the solution to impulsive differential hemivariational inequalities in relation to perturbation data. Finally, the existence and uniqueness of weak solution to the contact problem is proved by means of abstract results.</p>

中文翻译：

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一类历史相关准静态摩擦接触问题的脉冲半变分不等式

<p style='text-indent:20px;'>本文处理一类表面牵引受脉冲微分方程影响的历史相关摩擦接触问题。接触问题的弱表述是具有脉冲微分方程的与历史相关的半变分不等式。利用多值伪单调算子定理的满射性和Rothe方法，建立了抽象脉冲微分半变分不等式的存在唯一性结果。此外，我们考虑了与扰动数据相关的脉冲微分半变分不等式的解的稳定性。最后通过抽象结果证明了接触问题弱解的存在性和唯一性。</p>