Existence theorems of the hemivariational inequality governed by a multi-valued map perturbed with a nonlinear term in Banach spaces

Rabian Wangkeeree () and Pakkapon Preechasilp ()

Journal of Global Optimization, 2013, vol. 57, issue 4, 1447-1464

Abstract: In this paper, we establish some existence results for the hemivariational inequality governed by a multi-valued map perturbed with a nonlinear term in reflexive Banach spaces. Using the concept of the stable $$f$$ -quasimonotonicity, the properties of Clarke’s generalized directional derivative, Clarke’s generalized gradient and KKM technique, some existence theorems of solutions are proved when the constrained set is nonempty, bounded (or unbounded), closed and convex. Our main results extend various results existing in the current literatures. Copyright Springer Science+Business Media New York 2013

Keywords: Hemivariational inequality governed by a multi-valued map; Clarke’s generalized gradient; KKM technique; Banach space (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-0018-x

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