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Linear Fredholm Integral Equations and the Integral of Kurzweil
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M. Federson
Published/Copyright:
June 7, 2010
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.
Key words and phrases.: Linear integral equations; Fredholm Alternative; Kurzweil-Henstock integrals
Received: 2000-09-14
Revised: 2001-03-27
Published Online: 2010-06-07
Published in Print: 2002-June
© Heldermann Verlag
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- An Explicit Formula for Solutions of Some System of Linear Delay Difference Equations
- Existence and Controllability Results for Nonlinear Differential Inclusions with Nonlocal Conditions in Banach Spaces
- Results on Singular Distribution Products of Mikusiński Type
- A Quasistatic Contact Problem with Slip Dependent Coefficient of Friction for Elastic Materials
- Linear Fredholm Integral Equations and the Integral of Kurzweil
- On Trigonometric-Like Decompositions of Functions with Respect to the Cyclic Group of Order n
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Keywords for this article
Linear integral equations;
Fredholm Alternative;
Kurzweil-Henstock integrals
Articles in the same Issue
- The Infinite Dimensional Henstock Integral and Problems of Black-Scholes Expectation
- An Explicit Formula for Solutions of Some System of Linear Delay Difference Equations
- Existence and Controllability Results for Nonlinear Differential Inclusions with Nonlocal Conditions in Banach Spaces
- Results on Singular Distribution Products of Mikusiński Type
- A Quasistatic Contact Problem with Slip Dependent Coefficient of Friction for Elastic Materials
- Linear Fredholm Integral Equations and the Integral of Kurzweil
- On Trigonometric-Like Decompositions of Functions with Respect to the Cyclic Group of Order n
- The Existence and Uniqueness of Solution of One Coupled Plate Thermomechanics Problem
- On the Stationary Flow of the Power Law Fluid in 2D
