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THE SET OF SOLUTIONS OF INTEGRODIFFERENTIAL EQUATIONS IN BANACH SPACES

Part of: Stability theory

Published online by Cambridge University Press:  01 December 2008

RAVI P. AGARWAL ,
DONAL O’REGAN  and
ANETA SIKORSKA-NOWAK
RAVI P. AGARWAL
Affiliation:
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA (email: [email protected])
DONAL O’REGAN
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland (email: [email protected])
ANETA SIKORSKA-NOWAK
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland (email: [email protected])
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Abstract

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In this paper, we first prove an existence theorem for the integrodifferential equation (*)where f,k,x are functions with values in a Banach space E and the integral is taken in the sense of Henstock–Kurzweil–Pettis. In the second part of the paper we show that the set S of all solutions of the problem (*) is compact and connected in (C(Id,E),ω), where .

Keywords

integral equationsexistence theorempseudo-solutionset of solutionsmeasure of noncompactnessHenstock–Kurzweil–Pettis integral

MSC classification

Secondary: 34D09: Dichotomy, trichotomy 34D99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 3 , December 2008 , pp. 507 - 522
Copyright
Copyright © 2009 Australian Mathematical Society

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