EXISTENCE, UNIQUENESS AND REGULARITY OF THE SOLUTION FOR A SYSTEM OF WEAKLY SINGULAR VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND

Sedaghat Shahmorad; Mahdi Mostafazadeh

doi:10.1216/jie.2023.35.105

Abstract

The main purpose of this paper is to investigate the existence, uniqueness, and regularity of solutions for systems of linear and nonlinear weakly singular Volterra integral equations of the first kind, which have been stated as research problems (for the linear case) by Brunner (2017). To get these results, we first state sufficient conditions for the existence and uniqueness of solutions for a system of weakly singular Volterra integral equations of the second kind. We demonstrate the results by giving an example.

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Sedaghat Shahmorad. Mahdi Mostafazadeh. "EXISTENCE, UNIQUENESS AND REGULARITY OF THE SOLUTION FOR A SYSTEM OF WEAKLY SINGULAR VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND." J. Integral Equations Applications 35 (1) 105 - 117, Spring 2023. https://doi.org/10.1216/jie.2023.35.105

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Received: 28 August 2022; Accepted: 27 December 2022; Published: Spring 2023

First available in Project Euclid: 7 June 2023

MathSciNet: MR4598872

zbMATH: 07714672

Digital Object Identifier: 10.1216/jie.2023.35.105

Subjects:

Primary: 45A05 , 45D05 , 45E10 , 45F15

Keywords: existence and uniqueness of solution , first kind integral equations , System of singular integral equations

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