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Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 3
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Articles

Extremal solutions in systems of variational inequalities with multivalued mappings

Pages 561-573 | Received 28 Dec 2018, Accepted 22 Apr 2019, Published online: 09 May 2019
 

ABSTRACT

In this paper, we use a sub-supersolution method to study systems of variational inequalities of the form: Ak(uk)+Fk(u),vkuk0,vkKkukKk, (k=1,,m), where Ak and Fk are multivalued mappings with possibly non-power growths and Kk is a closed, convex set. We introduce a concept of mixed extremal solutions in the set-theoretic sense and prove the existence of such solutions between sub- and supersolutions. We also show the existence of least and greatest solutions of the above system between sub- and supersolutions if the lower order terms have certain increasing properties.

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2000 Mathematics Subject Classifications:

Acknowledgements

The author thanks the referees for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

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