Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On an extension of Minty's theorem

Author: Makoto Shimizu
Journal: Proc. Amer. Math. Soc. 114 (1992), 949-954
MSC: Primary 47H05; Secondary 47H04
MathSciNet review: 1079708
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] Viorel Barbu, Nonlinear semigroups and differential equations in Banach spaces, Editura Academiei Republicii Socialiste România, Bucharest; Noordhoff International Publishing, Leiden, 1976. Translated from the Romanian. MR 0390843
  • [2] H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1973 (French). North-Holland Mathematics Studies, No. 5. Notas de Matemática (50). MR 0348562
  • [3] Y. Kōmura, On the nonlinear semi-groups, Sûgaku 25 (1973), 148-160. (Japanese)
  • [4] George J. Minty, Monotone (nonlinear) operators in Hilbert space, Duke Math. J. 29 (1962), 341–346. MR 0169064
  • [5] Robert A. Bonic, Linear functional analysis, Notes on Mathematics and its Applications, Gordon and Breach Science Publishers, New York-London-Paris, 1969. MR 0257686

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H05, 47H04

Retrieve articles in all journals with MSC: 47H05, 47H04

Additional Information

Keywords: Extension, Minty's Theorem, Hilbert space
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society