Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces

Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces

We prove two existence theorems for the integrodifferential equation of mixed type: x'(t)=f(t,x(t),∫0tk1(t,s)g(s,x(s))ds,∫0ak2(t,s)h(s,x(s))ds), x(0)=x0, where in the first part of this paper f, g, h, x are functions with values in a Banach space E and integrals are taken in the sense of Hensto...

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Main Authors: Aneta Sikorska-Nowak, Grzegorz Nowak
Format: Article
Language:English
Published: Hindawi Limited 2007-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2007/65947
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spelling doaj-2987084fe0ee4e648cb74d5c564d5f7c2020-11-24T23:28:39ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/6594765947Nonlinear Integrodifferential Equations of Mixed Type in Banach SpacesAneta Sikorska-Nowak0Grzegorz Nowak1Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań 61-614, PolandUniversity of Marketing and Management, Ostroroga 9a, Leszno 64-100, PolandWe prove two existence theorems for the integrodifferential equation of mixed type: x'(t)=f(t,x(t),∫0tk1(t,s)g(s,x(s))ds,∫0ak2(t,s)h(s,x(s))ds), x(0)=x0, where in the first part of this paper f, g, h, x are functions with values in a Banach space E and integrals are taken in the sense of Henstock-Kurzweil (HK). In the second part f, g, h, x are weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis (HKP) integral. Additionally, the functions f, g, h, x satisfy some conditions expressed in terms of the measure of noncompactness or the measure of weak noncompactness.http://dx.doi.org/10.1155/2007/65947
collection DOAJ
language English
format Article
sources DOAJ
author Aneta Sikorska-Nowak
Grzegorz Nowak
spellingShingle Aneta Sikorska-Nowak
Grzegorz Nowak
Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces
International Journal of Mathematics and Mathematical Sciences
author_facet Aneta Sikorska-Nowak
Grzegorz Nowak
author_sort Aneta Sikorska-Nowak
title Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces
title_short Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces
title_full Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces
title_fullStr Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces
title_full_unstemmed Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces
title_sort nonlinear integrodifferential equations of mixed type in banach spaces
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2007-01-01
description We prove two existence theorems for the integrodifferential equation of mixed type: x'(t)=f(t,x(t),∫0tk1(t,s)g(s,x(s))ds,∫0ak2(t,s)h(s,x(s))ds), x(0)=x0, where in the first part of this paper f, g, h, x are functions with values in a Banach space E and integrals are taken in the sense of Henstock-Kurzweil (HK). In the second part f, g, h, x are weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis (HKP) integral. Additionally, the functions f, g, h, x satisfy some conditions expressed in terms of the measure of noncompactness or the measure of weak noncompactness.
url http://dx.doi.org/10.1155/2007/65947
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AT grzegorznowak nonlinearintegrodifferentialequationsofmixedtypeinbanachspaces
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