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Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

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1869-6090
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Weighted Lp -solutions on unbounded intervals of nonlinear integral equations of the Hammerstein and Urysohn types

Abderrazek Karoui / Adel Jawahdou / Hichem Ben Aouicha
  • University of Carthage, Department of Mathematics, Preparatory Institute of Engineering of Bizerte, Jarzouna 7021, Tunisia.
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Published Online: 2010-05-07 | DOI: https://doi.org/10.1515/apam.2010.021

Abstract

In this paper, we consider a positive real number p ≥ 1, a weight function μ(·) and give different existence results in the weighted Lp (ℝ+, )-space of some nonlinear integral equations of Hammerstein and Urysohn's types. It is well known that solving the existence problems of such equations on unbounded domains is more challenging than the case of a bounded domain. The main ingredient of our existence results is the Schauder's fixed point theorem. Hence, a special interest is devoted to the compactness as well as the continuity of the integral operators associated with the above integral equations. Moreover, some examples are provided to illustrate the different results of this work.

Keywords.: Nonlinear integral equations; Hammerstein's integral equation; Urysohn's integral equation; compact operators; Schauder's fixed point theorem

About the article

Received: 2010-01-02

Accepted: 2010-02-19

Published Online: 2010-05-07

Published in Print: 2011-01-01


Citation Information: Advances in Pure and Applied Mathematics, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam.2010.021.

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