Existence of solutions and $\alpha$-well-posedness for a system of constrained set-valued variational inequalities

Jiawei  Chen; Zhongping Wan; Liuyang Yuan

doi:10.3934/naco.2013.3.567

Article Contents

2013, Volume 3, Issue 3: 567-581. Doi: 10.3934/naco.2013.3.567

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Existence of solutions and $\alpha$-well-posedness for a system of constrained set-valued variational inequalities

1.
School of Mathematics and Statistics, Wuhan University, Wuhan 430072
2.
School of Mathematics and Statistics, Wuhan University, Wuhan, 430072

Received: August 31, 2011

Revised: March 31, 2013

Published: June 2013

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Abstract

The notions of $\alpha$-well-posedness and generalized $\alpha$-well-posedness for a system of constrained variational inequalities involving set-valued mappings (for short, (SCVI)) are introduced in Hilbert spaces. Existence theorems of solutions for (SCVI) are established by using penalty techniques. Metric characterizations of $\alpha$-well-posedness and generalized $\alpha$-well-posedness, in terms of the approximate solutions sets, are presented. Finally, the equivalences between (generalized) $\alpha$-well-posedness for (SCVI) and existence and uniqueness of its solutions are also derived under quite mild assumptions.

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Mathematics Subject Classification: Primary: 47J04, 49K40; Secondary: 90C31.

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