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, 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
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.
17 Feb 2021