Abstract
ABSTRACT In this paper, we use a sub-supersolution method to study systems of variational inequalities of the form: , where and are multivalued mappings with possibly non-power growths and 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.
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