A REGULARITY THEOREM FOR A VOLTERRA INTEGRAL EQUATION OF THE THIRD KIND

An existence and smoothness theorem is given for a Volterra integral equation of the form $\mathrm{f}\left(\mathrm{x}\right)\mathrm{v}\left(\mathrm{x}\right)=\mathrm{\phi }\left(\mathrm{x}\right)-{\int }_{0}^{\mathrm{x}}\mathrm{K}(\mathrm{x},\mathrm{\xi })\mathrm{v}\left(\mathrm{\xi }\right)\mathrm{...

Full description

Saved in:
Bibliographic Details
Published in:The Journal of integral equations and applications 2008-12, Vol.20 (4), p.507-526
Main Author: GRANDITS, PETER
Format: Article
Language:English
Subjects:
Coefficients
Continuous functions
Differential equations
Inhomogeneity
Mathematical functions
Mathematical integrals
Ordinary differential equations
Partial derivatives
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:An existence and smoothness theorem is given for a Volterra integral equation of the form $\mathrm{f}\left(\mathrm{x}\right)\mathrm{v}\left(\mathrm{x}\right)=\mathrm{\phi }\left(\mathrm{x}\right)-{\int }_{0}^{\mathrm{x}}\mathrm{K}(\mathrm{x},\mathrm{\xi })\mathrm{v}\left(\mathrm{\xi }\right)\mathrm{d}\mathrm{\xi }$ where f(x) has a zero at x = 0, and the kernel K(x, ξ) has a kind of square root behavior at the diagonal x = ξ.
ISSN:0897-3962
1938-2626
DOI:10.1216/JIE-2008-20-4-507