An invariance of domain result

for multi-valued maximal monotone

operators whose domains do not necessarily

contain any open sets

Author:
Athanassios G. Kartsatos

Journal:
Proc. Amer. Math. Soc. **125** (1997), 1469-1478

MSC (1991):
Primary 47H17; Secondary 47H05, 47H10

DOI:
https://doi.org/10.1090/S0002-9939-97-03739-8

MathSciNet review:
1371130

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Abstract: Let be a real, reflexive, locally uniformly convex Banach space with locally uniformly convex. Let be a maximal monotone operator and open and bounded. Assume that is pathwise connected and such that and Then If, moreover, is of type () on then may be replaced above by The significance of this result lies in the fact that it holds for multi-valued mappings which do not have to satisfy It has also been used in this paper in order to establish a general ``invariance of domain'' result for maximal monotone operators, and may be applied to a greater variety of problems involving partial differential equations. No degree theory has been used. In addition to the above, necessary and sufficient conditions are given for the existence of a zero (in an open and bounded set ) of a completely continuous perturbation of a maximal monotone operator such that is locally monotone on

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Additional Information

**Athanassios G. Kartsatos**

Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700

Email:
hermes@gauss.math.usf.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03739-8

Keywords:
Maximal monotone operator,
pathwise connected set,
invariance of domain,
compact perturbation,
existence of zeros

Received by editor(s):
September 12, 1995

Received by editor(s) in revised form:
November 27, 1995

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1997
American Mathematical Society