Solutions of integro-differential equations on the half-axis with rapidly decreasing non-difference kernels
type: Item
instance of: scholarly article
title: Solutions of integro-differential equations on the half-axis with rapidly decreasing non-difference kernels
zbMATH Open document ID: 1012.45005
author: Anna Mitina
published in: Journal of Integral Equations and Applications
publication date: 2002-10-14T00:00:00Z
full work available at URL: CONT13-4.html
review text: The author studies the set of all solutions of the integro-differential equation \[ -\frac{d^2 y}{dx^2} + y = \int^{\infty}_0 R_1 (x-t)y(t) dt + \int^{\infty}_0 R_2 (x+t)y(t) dt, \quad x>0 \] under various assumptions on the kernels \(R_1 (x)\) and \(R_2 (x)\). With the introduction of a large parameter \(\nu\), he is able to define the Cauchy problem and boundary value problems and also obtains a convenient algorithm for calculating the approximate solutions of these two problems.
reviewed by: James A. Oguntuase
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45L05
zbMATH DE Number: 1779506
zbMATH Keywords: integro-differential equation
zbMATH Keywords: Cauchy problem
zbMATH Keywords: boundary value problems
zbMATH Keywords: algorithm
zbMATH Keywords: approximate solutions
MaRDI profile type: Publication
OpenAlex ID: W2009797495
cites work: Q4236310
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cites work: Asymptotic behavior of the solutions of the integro-differential equations on positive half-axis with non-difference kernel of a certain type
cites work: Existence and uniqueness theorems for integro-differential equations on the half-axis with non-difference kernel of a certain type. Upper and lower bounds for solutions
cites work: Q5634307
cites work: The theory of the anomalous skin effect in metals
DOI: 10.1216/JIEA/1020254810
description: scientific article; zbMATH DE number 1779506