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Journal of Convex Analysis 32 (2025), No. 2, 545--564
Copyright Heldermann Verlag 2025



Unbounded Perturbation of History-Dependent Evolution Inclusion with Difference of Two Subdifferentials

Zhenhai Liu
(1) Center for Applied Mathematics of Guangxi,, Guangxi Minzu University, Nanning, Guangxi, P. R. China
(2) Center for Applied Mathematics of Guangxi, Yulin Normal University, P. R. China
zhhliu@hotmail.com

Sergey A. Timoshin
School of Mathematics and Physics, Xi'an Jiaotong-Liverpool University, Suzhou, Jiangsu, P. R. China
sergey.timoshin@gmail.com

Ze Yuan
School of Mathematics and Physics, Xi'an Jiaotong-Liverpool University, Suzhou, Jiangsu, P. R. China
2317802214@qq.com



We consider a perturbed hemivariational inequality with an additional negative subdifferential term and history-dependent operators. The perturbation is represented by a multivalued mapping, and its values are not assumed to be convex or bounded. We prove that there is a solution to our problem and establish a relaxation-approximation result for it using a localized version of Hausdorff-Lipschitz continuity adapted to the unbounded case.

Keywords: Unbounded perturbation, truncated Lipschitz condition, difference of subdifferentials, hemivariational inequality, history-dependent operators.

MSC: 47J20, 47J22, 49J40, 49J45, 49J52, 49J53.

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