Electron. J. Differential Equations, Vol. 2018 (2018), No. 19, pp. 1-20.

Solvability of nonlinear integral equations of product type

Bilal Boulfoul, Azzeddine Bellour, Smail Djebali

This article concerns nonlinear functional integral equations of product type. The first two equations set on a the positive half-axis encompass different classes of nonlinear integral equations and may involve the product of finitely many integral functions. The existence of integrable solutions is based on improved versions of Krasnoselskii's fixed point theorem combined with techniques of measure of weak noncompactness and some elements from functional analysis. The third one is an integro-differential equation set on a bounded interval, for which the existence of absolutely continuous solutions is provided. Examples show the applicability of our results.

Submitted July 21, 2017. Published January 15, 2018.
Math Subject Classifications: 45D05, 45G10, 47H08, 47H09, 47H10, 47H30.
Key Words: Product integral equation; measure of weak noncompactness; strict gamma-contraction; Krasnoselskii's fixed point theorem; Caratheodory's conditions; (ws)-compact; integrable solution; absolutely continuous solution.

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Bilal Boulfoul
Department of Mathematics
ESSA, Algiers, Algeria
email: bilal_maths@hotmail.com
Azzeddine Bellour
Department of Mathematics
ENS Constantine, Algeria
email: bellourazze123@yahoo.com
Smail Djebali
Department of Mathematics
faculty of Sciences
Al Imam Mohammad Ibn Saud Islamic University (IMSIU)
P.O. Box 90950, Riyadh 11623, Saudi Arabia.
email: djebali@hotmail.com

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