Monotone iterative sequences for non-local elliptic problems

Mohammed Al-Refai, Nikos I. Kavallaris, Mohamed Ali Hajji

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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 γ(the parameter of the problem). The convergence of the iterative sequence is tested through examples with an order of convergence greater than 1.

Original languageEnglish
Pages (from-to)533-552
Number of pages20
JournalEuropean Journal of Applied Mathematics
Issue number6
Publication statusPublished - Dec 2011


  • Elliptic Differential Equations
  • Maximum Principle
  • Non-Local Problems

ASJC Scopus subject areas

  • Applied Mathematics


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