Solutions to systems of linear Fredholm integral equations of the third kind
type: Item
instance of: scholarly article
title: Solutions to systems of linear Fredholm integral equations of the third kind
zbMATH Open document ID: 1204.45005
DOI: 10.1134/S1064562410010321
author: M. I. Imanaliev
author: A. Asanov
published in: Doklady Mathematics
publication date: 2010-11-17T00:00:00Z
review text: The authors simultaneously consider the systems of linear integral equations \[ Fu=f(t),\quad \varepsilon v(t,\varepsilon)+Fv=f(t),\quad t\in [t_0,T], \] where \(Fu=A(t)u(t)+ \int_{t_0}^TK(t,s)u(s)ds\), \(A(t)\) and \(K(t,s)\) are given \(n\times n\) matrix functions, \(f(t)\) is a given \(n\)-dimensional vector function, \(u(t)\) and \(v(t,\varepsilon)\) are the desired \(n\)-dimensional vector functions and \(0<\varepsilon \) is a small parameter. Under adequate conditions on \(A\) and \(K\) they demonstrate the uniqueness of the solutions \(u(t)\) and \(v(t,\varepsilon)\) and the convergence of \(v(t,\varepsilon)\) to \(u(t)\) as \(\varepsilon\to 0\). They also demonstrate the continuous dependence of the solutions \(u(t)\) and \(v(t,\varepsilon)\) on the right-hand side term \(f(t)\).
reviewed by: Adrian Carabineanu
Mathematics Subject Classification ID: 45F05
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 5816876
zbMATH Keywords: uniqueness
zbMATH Keywords: convergence
zbMATH Keywords: uniform continuity
zbMATH Keywords: Fredholm integral equations of the third kind
zbMATH Keywords: systems of linear integral equations
zbMATH Keywords: continuous dependence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5816876