Unbounded perturbation of an evolution hemivariational inequality

Zhenhai Liu; Chen Bin; Xiake Liu; Sergey A. Timoshin

doi:10.1016/j.nonrwa.2024.104070

Unbounded perturbation of an evolution hemivariational inequality

Zhenhai Liu, Chen Bin, Xiake Liu, Sergey A. Timoshin^*

^*Corresponding author for this work

Department of Applied Mathematics

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

Abstract

We consider a perturbed hemivariational inequality. The perturbation is a multivalued mapping the values thereof are not assumed to be convex or bounded. We prove the existence of a solution to our problem and establish a relaxation — approximation result for it through the use of a localized version of Hausdorff-Lipschitzness adapted to the unbounded case.

Original language	English
Article number	104070
Journal	Nonlinear Analysis: Real World Applications
Volume	77
DOIs	https://doi.org/10.1016/j.nonrwa.2024.104070
Publication status	Published - Jun 2024

Keywords

Evolution subdifferential inclusion
Hemivariational inequality
Truncated Lipschitz condition
Unbounded perturbation

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10.1016/j.nonrwa.2024.104070

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Liu, Z., Bin, C., Liu, X., & Timoshin, S. A. (2024). Unbounded perturbation of an evolution hemivariational inequality. Nonlinear Analysis: Real World Applications, 77, Article 104070. https://doi.org/10.1016/j.nonrwa.2024.104070

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abstract = "We consider a perturbed hemivariational inequality. The perturbation is a multivalued mapping the values thereof are not assumed to be convex or bounded. We prove the existence of a solution to our problem and establish a relaxation — approximation result for it through the use of a localized version of Hausdorff-Lipschitzness adapted to the unbounded case.",

keywords = "Evolution subdifferential inclusion, Hemivariational inequality, Truncated Lipschitz condition, Unbounded perturbation",

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AU - Bin, Chen

AU - Liu, Xiake

AU - Timoshin, Sergey A.

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N2 - We consider a perturbed hemivariational inequality. The perturbation is a multivalued mapping the values thereof are not assumed to be convex or bounded. We prove the existence of a solution to our problem and establish a relaxation — approximation result for it through the use of a localized version of Hausdorff-Lipschitzness adapted to the unbounded case.

AB - We consider a perturbed hemivariational inequality. The perturbation is a multivalued mapping the values thereof are not assumed to be convex or bounded. We prove the existence of a solution to our problem and establish a relaxation — approximation result for it through the use of a localized version of Hausdorff-Lipschitzness adapted to the unbounded case.

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KW - Hemivariational inequality

KW - Truncated Lipschitz condition

KW - Unbounded perturbation

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Unbounded perturbation of an evolution hemivariational inequality

Abstract

Keywords

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