Extremal Solutions in Systems of Variational Inequalities with Multivalued Mappings

Author

Vy Khoi Le, Missouri University of Science and TechnologyFollow

Abstract

In this paper, we use a sub-supersolution method to study systems of variational inequalities of the form: (Formula presented), where 𝓐_k and 𝓕_k are multivalued mappings with possibly non-power growths and K_k 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.

Recommended Citation

V. K. Le, "Extremal Solutions in Systems of Variational Inequalities with Multivalued Mappings," Applicable Analysis, vol. 100, no. 3, pp. 561 - 573, Taylor & Francis Ltd., Feb 2021.

The definitive version is available at https://doi.org/10.1080/00036811.2019.1612049

Department(s)

Mathematics and Statistics

Comments

Published online: 09 May 2019

Keywords and Phrases

C. Siegfried; Extremal solution; Multivalued mapping; Orlicz-Sobolev space; Sub-supersolution; System of variational inequalities

International Standard Serial Number (ISSN)

0003-6811; 1563-504X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019 Taylor & Francis Ltd., All rights reserved.

Publication Date

17 Feb 2021