An invariance of domain result for multivalued maximal monotone operators whose domains do not necessarily contain any open sets
Author:
Athanassios G. Kartsatos
Journal:
Proc. Amer. Math. Soc. 125 (1997), 14691478
MSC (1991):
Primary 47H17; Secondary 47H05, 47H10
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 multivalued 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 336205700
Email:
hermes@gauss.math.usf.edu
DOI:
http://dx.doi.org/10.1090/S0002993997037398
PII:
S 00029939(97)037398
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
