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

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

doi:10.1016/j.jmaa.2010.09.034

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

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

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	402-411
Number of pages	10
Journal	Journal of Mathematical Analysis and Applications
Volume	374
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2010.09.034
Publication status	Published - Feb 15 2011

Keywords

Elliptic equations
Maximum principle
Upper and lower solutions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2010.09.034

Cite this

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title = "Analytical sequences of upper and lower solutions for a class of elliptic equations",

abstract = "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.",

keywords = "Elliptic equations, Maximum principle, Upper and lower solutions",

author = "Mohammed Al-Refai and Muhammed Syam and Qasem Al-Mdallal",

note = "Funding Information: The authors would like to express their sincere appreciation to the Research Affairs at the United Arab Emirates University for the financial support of these projects under fund grants Nos. 01−13−02−11/07,05−13−02−11/08 and 04−13−02−11/07.",

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T1 - Analytical sequences of upper and lower solutions for a class of elliptic equations

AU - Al-Refai, Mohammed

AU - Syam, Muhammed

AU - Al-Mdallal, Qasem

N1 - Funding Information: The authors would like to express their sincere appreciation to the Research Affairs at the United Arab Emirates University for the financial support of these projects under fund grants Nos. 01−13−02−11/07,05−13−02−11/08 and 04−13−02−11/07.

PY - 2011/2/15

Y1 - 2011/2/15

N2 - 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.

AB - 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.

KW - Elliptic equations

KW - Maximum principle

KW - Upper and lower solutions

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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