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On an extension of Minty's theorem


Author: Makoto Shimizu
Journal: Proc. Amer. Math. Soc. 114 (1992), 949-954
MSC: Primary 47H05; Secondary 47H04
DOI: https://doi.org/10.1090/S0002-9939-1992-1079708-9
MathSciNet review: 1079708
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Abstract: The notion of monotone operator in a Hilbert space is extended, and a considerably broader class of possibly multivalued operators is introduced. It is shown that well-known Minty's theorems on maximal monotone operators in Hilbert spaces can be extended to the cases of operators belonging to the class. Typical examples of partial differential operators are given to illustrate that the results can be applied to nonlinear equations, which involve nonmonotone differential operators.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1079708-9
Keywords: Extension, Minty's Theorem, Hilbert space
Article copyright: © Copyright 1992 American Mathematical Society

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