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

Published online by Cambridge University Press:  21 July 2016

REZA ALLAHYARI
Affiliation:
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran email [email protected]
REZA ARAB*
Affiliation:
Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran email [email protected]
ALI SHOLE HAGHIGHI
Affiliation:
Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran email [email protected]
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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.

Type
Research Article
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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