Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter June 7, 2010

Linear Fredholm Integral Equations and the Integral of Kurzweil

M. Federson and R. Bianconi

Abstract

We apply the Kurzweil-Henstock integral setting to prove a Fredholm Alternative-type result for the integral equation

x (t) – K[a, b]α (t, s) x (s) ds = ƒ (t), t ∈ [a, b],

where x and ƒ are Kurzweil integrable functions (possibly highly oscillating) defined on a compact interval [a, b] of the real line with values on Banach spaces. An application is given.

Received: 2000-09-14
Revised: 2001-03-27
Published Online: 2010-06-07
Published in Print: 2002-June

© Heldermann Verlag