Extremal solutions in systems of variational inequalities with multivalued mappings. Issue 3 (17th February 2021)

• Record Type: Journal Article
• Authors: Le, Vy Khoi
• Is Part Of: Applicable analysis. Volume 100:Issue 3(2021)
• Page Start: 561
• Page End: 573
• Publication Date: 2021-02-17
• Subjects: C. Siegfried; System of variational inequalities -- multivalued mapping -- sub-supersolution -- extremal solution -- Orlicz–Sobolev space; Primary: 35B45 -- 35J65 -- 35J60; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1612049
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we use a sub-supersolution method to study systems of variational inequalities of the form: ⟨ A k ( u k ) + F k ( u ), v k − u k ⟩ ≥ 0, ∀ v k ∈ K k u k ∈ K k, ( k = 1, …, m ), 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.