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

Zhenhai Liu; Sergey A. Timoshin; Ze Yuan

Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

Unbounded perturbation
truncated Lipschitz condition
difference of subdifferentials
hemivariational inequality
history-dependent operators

Mathematics Subject Classification

47J20, 47J22, 49J40, 49J45, 49J52, 49J53

Suggested citation

Z. Liu, S. A. Timoshin, Z. Yuan. “Unbounded Perturbation of History-Dependent Evolution Inclusion with Difference of Two Subdifferentials.” Journal of Convex Analysis 32 (2025), No. 2, 545–564.