On the perturbation theory of accretive operators in Banach spaces
Author:
Athanassios G. Kartsatos
Journal:
Proc. Amer. Math. Soc. 124 (1996), 18111820
MSC (1991):
Primary 47H17; Secondary 47B44, 47H09, 47H10
MathSciNet review:
1327021
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Let be a real Banach space. Let be accretive with compact. Let be such that is condensing for some Let and assume that there exists a bounded open set and such that is bounded and for all Then A basic homotopy result of the degree theory for with condensing and possibly unbounded, is used to improve and/or extend recent results by Hirano and Kalinde.
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 [1]
 V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff Int. Publ., Leyden (The Netherlands), 1975.
 [2]
 F. E. Browder, Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces, Proc. Symp. Pure Appl. Math., 18, Part 2, Providence, 1976. MR 53:8982
 [3]
 Y. Z. Chen, The generalized degree for compact perturbations of accretive operators and applications, Nonl. Anal. TMA 13 (1989), 393403. MR 90c:47094
 [4]
 I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Kluwer Acad. Publ., Boston, 1990. MR 91m:46021
 [5]
 K. Deimling, Nonlinear Functional Analysis, SpringerVerlag, New York, 1985. MR 86j:47001
 [6]
 Z. Ding and A. G. Kartsatos, Nonzero solutions of nonlinear equations involving compact perturbations of accretive operators in Banach spaces, Nonl. Anal. TMA 25 (1995), 13331342.
 [7]
 Z. Guan, Ranges of operators of monotone type in Banach spaces, J. Math. Anal. Appl. 174 (1993), 256264. MR 95b:47068
 [8]
 Z. Guan, Solvability of semilinear equations with compact perturbations of operators of monotone type, Proc. Amer. Math. Soc. 121 (1994), 93102. MR 94g:47080
 [9]
 Z. Guan and A. G. Kartsatos, Solvability of nonlinear equations with coercivity generated by compact perturbations of accretive operators in Banach spaces, Houston J. Math. 21 (1995), 149188.
 [10]
 Z. Guan and A. G. Kartsatos, Ranges of perturbed maximal monotone and accretive operators in Banach spaces, Trans. Amer. Math. Soc. 347 (1995), 24032435. CMP 95:02
 [11]
 N. Hirano and A. K. Kalinde, On perturbations of accretive operators in Banach spaces, Proc. Amer. Math. Soc. (to appear). CMP 95:03
 [12]
 D. R. Kaplan and A. G. Kartsatos, Ranges of sums and control of nonlinear evolutions with preassigned responses, J. Opt. Th. Appl. 81 (1994), 121141. CMP 94:12
 [13]
 A. G. Kartsatos, On compact perturbations and compact resolvents of nonlinear maccretive operators in Banach spaces, Proc. Amer. Math. Soc. 119 (1993), 11891199. MR 94c:47076
 [14]
 A. G. Kartsatos, Recent results involving compact perturbations and compact resolvents of accretive operators in Banach spaces, Proceedings of the First World Congress of Nonlinear Analysts, Tampa, Florida, 1992, Walter De Gruyter, New York, 1995, pp. 21972222.
 [15]
 A. G. Kartsatos, On the construction of methods of lines for functional evolutions in general Banach spaces, Nonl. Anal. TMA 25 (1995), 13211331.
 [16]
 A. G. Kartsatos, A compact evolution operator generated by a timedependent accretive operator in a general Banach space, Math. Ann. 302 (1995), 473487. CMP 94:12
 [17]
 A. G. Kartsatos, New results in the perturbations theory of maximal monotone and accretive operators in Banach spaces, Trans. Amer. Math. Soc. (to appear).
 [18]
 V. Lakshmikantham and S. Leela, Nonlinear Differential Equations in Abstract Spaces, Pergamon Press, Oxford, 1981. MR 82i:34072
 [19]
 N. G. Liu, The generalized degree for set contracting perturbation of accretive operator and applications, Nonl. Anal. TMA 18 (1992), 605618. MR 93g:47077
 [20]
 N. G. Lloyd, Degree Theory, Cambridge Univ. Press, Cambridge, 1978. MR 58:12558
 [21]
 M. Nagumo, Degree of mapping in convex linear topological spaces, Amer. J. Math. 73 (1951), 497511. MR 13:150b
 [22]
 W. V. Petryshyn, ApproximationSolvability of Nonlinear Functional and Differential Equations, Marcel Dekker, New York, 1993. MR 94f:47081
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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/S0002993996033497
PII:
S 00029939(96)033497
Keywords:
Accretive operator,
$m$accretive operator,
compact perturbation,
compact resolvent,
degree theory for condensing mappings
Received by editor(s):
December 5, 1994
Communicated by:
Palle E. T. Jorgensen
Article copyright:
© Copyright 1996 American Mathematical Society
