Analytical sequences of upper and lower solutions for a class of elliptic equations

Mohammed Al-Refai, Muhammed Syam, Qasem Al-Mdallal

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Comparison arguments are applied to derive decreasing sequences of upper solutions and increasing sequences of lower solutions for a class of nonlinear elliptic equations. The monotonicity of the two sequences is proven. These polynomial sequences are obtained by applying new algorithms and solving linear differential equations. The obtained upper and lower solutions are analytic and have closed forms. Different examples are presented to explore the effectiveness of the new algorithms. The presented ideas and algorithms can be extended to deal with different classes of equations.

Original languageEnglish
Pages (from-to)402-411
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - Feb 15 2011


  • Elliptic equations
  • Maximum principle
  • Upper and lower solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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