Unbounded perturbation of history-dependent evolution inclusion with difference of two subdifferentials

Zhenhai Liu; Sergey A. Timoshin; Ze Yuan

Unbounded perturbation of history-dependent evolution inclusion with difference of two subdifferentials

Zhenhai Liu, Sergey A. Timoshin^*, Ze Yuan

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	545-564
Journal	Journal of Convex Analysis
Volume	35
Issue number	2
Publication status	Published - 1 Apr 2025

Keywords

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

Cite this

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title = "Unbounded perturbation of history-dependent evolution inclusion with difference of two subdifferentials",

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.",

keywords = "difference of subdifferentials, hemivariational inequality, history-dependent operators, truncated Lipschitz condition, Unbounded perturbation",

author = "Zhenhai Liu and Timoshin, \{Sergey A.\} and Ze Yuan",

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AU - Liu, Zhenhai

AU - Timoshin, Sergey A.

AU - Yuan, Ze

N1 - Publisher Copyright: © Heldermann Verlag.

PY - 2025/4/1

Y1 - 2025/4/1

N2 - 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.

AB - 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.

KW - difference of subdifferentials

KW - hemivariational inequality

KW - history-dependent operators

KW - truncated Lipschitz condition

KW - Unbounded perturbation

UR - https://www.scopus.com/pages/publications/105006549141

M3 - Article

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SN - 0944-6532

VL - 35

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EP - 564

JO - Journal of Convex Analysis

JF - Journal of Convex Analysis

IS - 2

ER -

Unbounded perturbation of history-dependent evolution inclusion with difference of two subdifferentials

Abstract

Keywords

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