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MEASURES OF NONCOMPACTNESS IN A SOBOLEV SPACE AND INTEGRO-DIFFERENTIAL EQUATIONS

Part of: Nonlinear operators and their properties Integro-ordinary differential equations Miscellaneous special kernels

Published online by Cambridge University Press:  21 July 2016

REZA ALLAHYARI ,
REZA ARAB  and
ALI SHOLE HAGHIGHI
REZA ALLAHYARI
Affiliation:
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran email rezaallahyari@mshdiau.ac.ir
REZA ARAB*
Affiliation:
Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran email mathreza.arab@iausari.ac.ir
ALI SHOLE HAGHIGHI
Affiliation:
Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran email ali.sholehaghighi@gmail.com
*
✉mathreza.arab@iausari.ac.ir
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Abstract

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The aim of this paper is to introduce a new measure of noncompactness on the Sobolev space $W^{n,p}[0,T]$. As an application, we investigate the existence of solutions for some classes of functional integro-differential equations in this space using Darbo’s fixed point theorem.

Keywords

measures of noncompactnessDarbo’s fixed point theoremintegro-differential equationsSobolev spaces

MSC classification

Primary: 47H08: Measures of noncompactness and condensing mappings, $K$-set contractions, etc.
Secondary: 45J05: Integro-ordinary differential equations 47H10: Fixed-point theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 3 , December 2016 , pp. 497 - 506
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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