New results in the perturbation theory of

maximal monotone and -accretive

operators in Banach spaces

Author:
Athanassios G. Kartsatos

Journal:
Trans. Amer. Math. Soc. **348** (1996), 1663-1707

MSC (1991):
Primary 47H17; Secondary 47B44, 47H09, 47H10

DOI:
https://doi.org/10.1090/S0002-9947-96-01654-6

MathSciNet review:
1357397

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a real Banach space and a bounded, open and convex subset of The solvability of the fixed point problem in is considered, where is a possibly discontinuous -dissipative operator and is completely continuous. It is assumed that is uniformly convex, and A result of Browder, concerning single-valued operators that are either uniformly continuous or continuous with uniformly convex, is extended to the present case. Browder's method cannot be applied in this setting, even in the single-valued case, because there is no class of permissible homeomorphisms. Let The effect of a weak boundary condition of the type on the range of operators is studied for -accretive and maximal monotone operators Here, with sufficiently large norm and Various new eigenvalue results are given involving the solvability of with respect to Several results do not require the continuity of the operator Four open problems are also given, the solution of which would improve upon certain results of the paper.

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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/S0002-9947-96-01654-6

Keywords:
$m$-accretive operator,
maximal monotone operator,
compact perturbation,
compact resolvent,
eigenvalues for nonlinear operators,
fixed point theory,
degree theory

Received by editor(s):
February 7, 1995

Additional Notes:
The results of this paper were announced in a lecture at the International Conference on Nonlinear Differential Equations, Kiev, Ukraine, August 21-27, 1995.

Article copyright:
© Copyright 1996
American Mathematical Society