Extremal solutions in systems of variational inequalities with multivalued mappings. Issue 3 (17th February 2021) - Le, Vy Khoi
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.