Integrodifferential equations of Volterra type with nonlocal and impulsive conditions

Amadou Diop; Moustapha Dieye; Mamadou Abdoul Diop; Khalil Ezzinbi

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

$\left\{ {\matrix{ {{{dx} \over {dt}}(t) = A(t)x(t) + \smallint _0^t{\rm{\Gamma }}(t,s)x(s)ds + f(t,x(t)),\quad } & {t \in I = [0,T],t \ne {t_i},i = 1,2,3, \ldots ,m,} \cr {x(t_i^ + ) = x({t_i}) + {J_i}(x({t_i})),\quad } & {} \cr {x(0) = {x_0} + g(x),\quad } & {} \cr } } \right.$

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.

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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

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Received: 15 May 2021; Accepted: 19 July 2021; Published: Spring 2022

First available in Project Euclid: 11 April 2022

MathSciNet: MR4406233

zbMATH: 1493.45013

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

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