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elliptic differential equations

European Journal of Applied Mathematics (1)

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Monotone iterative sequences for non-local elliptic problems
MOHAMMED AL-REFAI, NIKOS I. KAVALLARIS, MOHAMED ALI HAJJI
Journal:

European Journal of Applied Mathematics / Volume 22 / Issue 6 / December 2011

Published online by Cambridge University Press:

20 July 2011, pp. 533-552
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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.