Electron. J. Diff. Eqns., Vol. 2006(2006), No. 57, pp. 1-11.

Existence of solutions of an integral equation of Chandrasekhar type in the theory of radiative transfer

Josefa Caballero, Angelo B. Mingarelli, Kishin Sadarangani

Abstract:
We give an existence theorem for some functional-integral equations which includes many key integral and functional equations that arise in nonlinear analysis and its applications. In particular, we extend the class of characteristic functions appearing in Chandrasekhar's classical integral equation from astrophysics and retain existence of its solutions. Extensive use is made of measures of noncompactness and abstract fixed point theorems such as Darbo's theorem.

Submitted March 3, 2006. Published May 1, 2006.
Math Subject Classifications: 45M99, 47H09.
Key Words: Measure of noncompactness; Banach algebra; integral equation; functional equation; fixed point; Volterra; Chandrasekhar H-functions; Chandrasekhar integral equation; radiative transfer.

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Josefa Caballero
Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria
Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain
email: jmena@ull.es
Angelo B. Mingarelli
School of Mathematics and Statistics
Carleton University, Ottawa, Ontario, K1S 5B6, Canada
email: amingare@math.carleton.ca
Kishin Sadarangani
Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria
Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain
email: ksadaran@dma.ulpgc.es

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