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Weighted Lp-solutions on unbounded intervals of nonlinear integral equations of the Hammerstein and Urysohn types
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Abderrazek Karoui
,
Adel Jawahdou
Published/Copyright:
May 7, 2010
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+, dμ)-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
Received: 2010-01-02
Accepted: 2010-02-19
Published Online: 2010-05-07
Published in Print: 2011-January
© de Gruyter 2010
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Keywords for this article
Nonlinear integral equations;
Hammerstein's integral equation;
Urysohn's integral equation;
compact operators;
Schauder's fixed point theorem
Articles in the same Issue
- Weighted Lp-solutions on unbounded intervals of nonlinear integral equations of the Hammerstein and Urysohn types
- Harmonic analysis associated with the Cherednik operators and the Heckman–Opdam theory
- Solutions to conjugate Beltrami equations and approximation in generalized Hardy spaces
- Toeplitz operators with L1 symbols on Bergman spaces in the unit ball of
- On the boundedness of pseudo-differential operators associated with the Dunkl transform on the real line
- Equivalences induced by n-self-cotilting comodules
