Extremal Solutions in Systems of Variational Inequalities with Multivalued Mappings
In this paper, we use a sub-supersolution method to study systems of variational inequalities of the form: (Formula presented), 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.
V. K. Le, "Extremal Solutions in Systems of Variational Inequalities with Multivalued Mappings," Applicable Analysis, Taylor & Francis Ltd., May 2019.
The definitive version is available at https://doi.org/10.1080/00036811.2019.1612049
Mathematics and Statistics
Keywords and Phrases
C. Siegfried; extremal solution; multivalued mapping; Orlicz-Sobolev space; sub-supersolution; System of variational inequalities
International Standard Serial Number (ISSN)
Article - Journal
© 2019 Taylor & Francis Ltd., All rights reserved.
01 May 2019