Existence theorems of the variational-hemivariational inequalities

Guo-ji Tang and Nan-jing Huang ()

Journal of Global Optimization, 2013, vol. 56, issue 2, 605-622

Abstract: This paper is devoted to the existence of solutions for the variational-hemivariational inequalities in reflexive Banach spaces. Using the notion of the stable $${\phi}$$ -quasimonotonicity and the properties of Clarke’s generalized directional derivative and Clarke’s generalized gradient, some existence results of solutions are proved when the constrained set is nonempty, bounded (or unbounded), closed and convex. Moreover, a sufficient condition to the boundedness of the solution set and a necessary and sufficient condition to the existence of solutions are also derived. The results presented in this paper generalize and improve some known results. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Hemivariational inequality; Generalized monotonicity; KKM mapping; Existence (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-012-9884-5

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