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Monotone iterative sequences for non-local elliptic problems

Published online by Cambridge University Press:  20 July 2011

MOHAMMED AL-REFAI ,
NIKOS I. KAVALLARIS  and
MOHAMED ALI HAJJI
MOHAMMED AL-REFAI
Affiliation:
Department of Mathematical Science, United Arab Emirates University, P.O. Box 17551, Al Ain, UAE email: m_alrefai@uaeu.ac.ae, mahajji@uaeu.ac.ae
NIKOS I. KAVALLARIS
Affiliation:
Department of Statistics and Actuarial-Financial Mathematics, University of Aegean, TGr-83200 Karlovassi, Samos, Greece email: nkaval@aegean.gr
MOHAMED ALI HAJJI
Affiliation:
Department of Mathematical Science, United Arab Emirates University, P.O. Box 17551, Al Ain, UAE email: m_alrefai@uaeu.ac.ae, mahajji@uaeu.ac.ae
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Abstract

In this paper we establish an existence and uniqueness result for a class of non-local elliptic differential equations with the Dirichlet boundary conditions, which, in general, do not accept a maximum principle. We introduce one monotone sequence of lower–upper pairs of solutions and prove uniform convergence of that sequence to the actual solution of the problem, which is the unique solution for some range of λ (the parameter of the problem). The convergence of the iterative sequence is tested through examples with an order of convergence greater than 1.

Keywords

Non-Local ProblemsMaximum PrincipleElliptic Differential Equations
Type
Papers
Information
European Journal of Applied Mathematics , Volume 22 , Issue 6 , December 2011 , pp. 533 - 552
Copyright
Copyright © Cambridge University Press 2011

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