Eventually constant solutions of a rational difference equation

We describe all the solutions of a rational difference equation from Putnam’s mathematical competition, which are eventually equal to its positive equilibrium x ¯ = 1 . As a consequence we give a new, elegant and short proof of the fact that the equation has a positive solution which is not eventual...

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Bibliographic Details
Published in:Applied mathematics and computation 2009-09, Vol.215 (2), p.854-856
Main Authors: IRICANIN, Bratislav, STEVIC, Stevo
Format: Article
Language:English
Subjects:
Difference and functional equations, recurrence relations
Eventually equal to unity
Exact sciences and technology
Finite differences and functional equations
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Positive solutions
Rational difference equation
Sciences and techniques of general use
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Summary:We describe all the solutions of a rational difference equation from Putnam’s mathematical competition, which are eventually equal to its positive equilibrium x ¯ = 1 . As a consequence we give a new, elegant and short proof of the fact that the equation has a positive solution which is not eventually equal to one. Moreover, we show that almost all solutions of the equation are not eventually equal to one.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2009.05.044