Analytical sequences of upper and lower solutions for a class of elliptic equations |
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Authors: | Mohammed Al-Refai Muhammed Syam |
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Institution: | Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 17551, Al Ain, United Arab Emirates |
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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. |
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Keywords: | Maximum principle Upper and lower solutions Elliptic equations |
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