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In this paper, we are devoted to exploring conditions of well-posedness for generalized hemivariational inequalities with Clarke’s generalized directional derivative in reflexive Banach spaces. By using some equivalent formulations of the generalized hemivariational inequality with Clarke’s generalized directional derivative under different monotonicity assumptions, we establish two kinds of conditions under which the strong α-well-posedness and the weak α-well-posedness for the generalized hemivariational inequality with Clarke’s generalized directional derivative are equivalent to the existence and uniqueness of its solution, respectively. c ©2016 All rights reserved.

Some equivalence results for well-posedness of generalized hemivariational inequalities with clarkes generalized directional derivative