On an extension of Minty’s theorem
HTML articles powered by AMS MathViewer
- by Makoto Shimizu PDF
- Proc. Amer. Math. Soc. 114 (1992), 949-954 Request permission
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
- 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, DOI 10.1007/978-94-010-1537-0
- H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Mathematics Studies, No. 5, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1973 (French). MR 0348562 Y. Kōmura, On the nonlinear semi-groups, Sûgaku 25 (1973), 148-160. (Japanese)
- George J. Minty, Monotone (nonlinear) operators in Hilbert space, Duke Math. J. 29 (1962), 341–346. MR 169064
- Robert A. Bonic, Linear functional analysis, Notes on Mathematics and its Applications, Gordon and Breach Science Publishers, New York-London-Paris, 1969. MR 0257686
Additional Information
- © Copyright 1992 American Mathematical Society
- 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