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 |
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Pages (from-to) | 402-411 |
Number of pages | 10 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 374 |
Issue number | 2 |
DOIs | |
Publication status | Published - Feb 15 2011 |
Keywords
- Elliptic equations
- Maximum principle
- Upper and lower solutions
ASJC Scopus subject areas
- Analysis
- Applied Mathematics