An integral equation associated with linear homogeneous differential equations
type: Item
instance of: scholarly article
title: An integral equation associated with linear homogeneous differential equations
zbMATH Open document ID: 0595.34005
DOI: 10.1155/S0161171286000509
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46077
review text: Summary: Associated with each linear homogeneous differential equation \(y^{(n)}=\sum^{n-1}_{i=0}a_ i(x)y^{(i)}\) of order n on the real line, there is an equivalent integral equation \[ f(x)=f(x_ 0)+\int^{x}_{x_ 0}h(u)du+\int^{x}_{x_ 0}[\int^{u}_{x_ 0}G_{n-1}(u,v)a_ 0(v)f(v)dv]du \] which is satisfied by each solution f(x) of the differential equation.
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 45J05
zbMATH DE Number: 3957650
zbMATH Keywords: variation of parameters formula
zbMATH Keywords: uniform convergence
zbMATH Keywords: linear homogeneous differential equation
Wikidata QID: Q115243307
author: Anil K. Bose
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3957650