A class of differential hemivariational inequalities constrained on nonconvex star-shaped sets

Abstract

The purpose of this paper is to investigate a class of nonconvex-constrained differential hemivariational inequalities consisting of nonlinear evolution equations and evolutionary hemivariational inequalities. The admissible set of constraints is closed and star-shaped with respect to a certain ball in a reflexive Banach space. We construct an auxiliary inclusion problem and obtain the existence results by applying a surjectivity theorem for multivalued pseudomonotone operators and the properties of Clarke subgradient operator. Moreover, the existence of a solution to the original problem is established by hemivariational inequality approach and a penalization method in which a small parameter does not have to tend to zero. Finally, an application of the main results is provided.

Keywords:

• Differential hemivariational inequality
• Clarke subgradient
• star-shaped set
• surjectivity result
• penalization method

AMS Subject Classifications:

• 34G20
• 47J20
• 49J40
• 49J52

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This project is supported by the National Natural Science Foundation of China [grant number 12001120], Guangxi Natural Science Foundation [grant numbers 2021GXNSFAA075022, 2022GXNSFAA035617] Middle-aged and Young Teachers' Basic Ability Promotion Project of Guangxi [grant number 2020KY16017], Guangxi Key Laboratory of Quantity Economics, Guangxi First-class Discipline Statistics Construction Project Fund [grant numbers 2022SXZD02, 2022SXKCSZ02].