The set of solutions of integrodifferential equations in banach spaces

Ravi P. Agarwal; Donal O'Regan; Aneta Sikorska-Nowak

doi:10.1017/S0004972708000944

The set of solutions of integrodifferential equations in banach spaces

Ravi P. Agarwal
, Donal O'Regan
, Aneta Sikorska-Nowak

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

10 Citations (Scopus)

Abstract

In this paper, we first prove an existence theorem for the integrodifferential equation Equation presented 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(I _d,E),ω), where I_d ⊂ I_a.

Original language	English
Pages (from-to)	507-522
Number of pages	16
Journal	Bulletin of the Australian Mathematical Society
Volume	78
Issue number	3
DOIs	https://doi.org/10.1017/S0004972708000944
Publication status	Published - 1 Dec 2008

Keywords

Henstock-Kurzweil-Pettis integral
existence theorem
integral equations
measure of noncompactness
pseudo-solution
set of solutions

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Agarwal, RP;O'Regan, D;Sikorska-Nowak, A

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10.1017/S0004972708000944

Cite this

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abstract = "In this paper, we first prove an existence theorem for the integrodifferential equation Equation presented 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(I d,E),ω), where Id ⊂ Ia.",

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AU - Agarwal, Ravi P.

AU - O'Regan, Donal

AU - Sikorska-Nowak, Aneta

PY - 2008/12/1

Y1 - 2008/12/1

N2 - In this paper, we first prove an existence theorem for the integrodifferential equation Equation presented 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(I d,E),ω), where Id ⊂ Ia.

AB - In this paper, we first prove an existence theorem for the integrodifferential equation Equation presented 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(I d,E),ω), where Id ⊂ Ia.

KW - Henstock-Kurzweil-Pettis integral

KW - existence theorem

KW - integral equations

KW - measure of noncompactness

KW - pseudo-solution

KW - set of solutions

UR - https://www.scopus.com/pages/publications/77952322913

U2 - 10.1017/S0004972708000944

DO - 10.1017/S0004972708000944

M3 - Article

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VL - 78

SP - 507

EP - 522

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 3

ER -

The set of solutions of integrodifferential equations in banach spaces

Abstract

Keywords

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