期刊
OPTIMIZATION
卷 -, 期 -, 页码 -出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/02331934.2023.2175614
关键词
Differential hemivariational inequality; Clarke subgradient; star-shaped set; surjectivity result; penalization method
The paper investigates 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. The existence results are obtained by constructing an auxiliary inclusion problem and 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 the hemivariational inequality approach and a penalization method. A provided application of the main results.
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.
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