Existence Theorems for Elliptic and Evolutionary Variational and Quasi-Variational Inequalities

Akhtar A. Khan () and Dumitru Motreanu ()
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Akhtar A. Khan: Rochester Institute of Technology
Dumitru Motreanu: Université de Perpignan

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 3, No 21, 1136-1161

Abstract: Abstract This paper gives new existence results for elliptic and evolutionary variational and quasi-variational inequalities. Specifically, we give an existence theorem for evolutionary variational inequalities involving different types of pseudo-monotone operators. Another existence result embarks on elliptic variational inequalities driven by maximal monotone operators. We propose a new recessivity assumption that extends all the classical coercivity conditions. We also obtain criteria for solvability of general quasi-variational inequalities treating in a unifying way elliptic and evolutionary problems. Two of the given existence results for evolutionary quasi-variational inequalities rely on Mosco-type continuity properties and Kluge’s fixed point theorem for set-valued maps. We also focus on the case of compact constraints in the evolutionary quasi-variational inequalities. Here a relevant feature is that the underlying space is the domain of a linear, maximal monotone operator endowed with the graph norm. Applications are also given.

Keywords: Quasi-variational inequalities; Variational inequalities; Hemivariational inequalities; Monotone; Pseudo-monotone; Generalized pseudo-monotone; Coercivity; Asymptotic recessivity; 49J20; 90C51; 90C30 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-015-0825-6

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