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Spring 2022 Integrodifferential equations of Volterra type with nonlocal and impulsive conditions
Amadou Diop, Moustapha Dieye, Mamadou Abdoul Diop, Khalil Ezzinbi
J. Integral Equations Applications 34(1): 19-37 (Spring 2022). DOI: 10.1216/jie.2022.34.19

Abstract

This work is devoted to the study of a class of nonlocal impulsive integrodifferential equations of Volterra type. We investigate the situation when the resolvent operator corresponding to the linear part of

{dxdt(t)=A(t)x(t)+0tΓ(t,s)x(s)ds+f(t,x(t)),tI=[0,T],tti,i=1,2,3,,m,x(ti+)=x(ti)+Ji(x(ti)),x(0)=x0+g(x),

is norm continuous. Our results are obtained by using the Hausdorff measure of noncompactness and fixed point theorems. An example is provided to illustrate the basic theory of this work.

Citation

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Amadou Diop. Moustapha Dieye. Mamadou Abdoul Diop. Khalil Ezzinbi. "Integrodifferential equations of Volterra type with nonlocal and impulsive conditions." J. Integral Equations Applications 34 (1) 19 - 37, Spring 2022. https://doi.org/10.1216/jie.2022.34.19

Information

Received: 15 May 2021; Accepted: 19 July 2021; Published: Spring 2022
First available in Project Euclid: 11 April 2022

Digital Object Identifier: 10.1216/jie.2022.34.19

Subjects:
Primary: 34B37 , 34G25 , 47H08

Keywords: Integrodifferential equations , Mönch’s fixed point , operator norm continuity , resolvent operator

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.34 • No. 1 • Spring 2022
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