Abstract: In this paper, we introduce and study a new class of evolutionary dierential
hemivariational inequalities in Banach spaces. Using a fixed-point theorem, we first establish
the existence and uniqueness of mild solutions for the evolutionary dierential hemivariational
inequality. Building on this result, we then investigate the stability of the evolutionary differential
hemivariational inequality problem under perturbations of the mappings, constraint
set, and infinitesimal generator of the C^0-semigroup e^{tB}.

Key words: evolutionary differential hemivariational inequality, mild solution, stability, C^0-
semigroup