Symmetric functions and difference equations with asymptotically period-two solutions

This paper introduces easily verified conditions which guarantee that all solutions to the equation [Y.sub.n] = f([Y.sub.n-k], [Y.sub.n-m]), with k,m [greater than or equal to] 1 and gcd(k,m) = 1 are asymptotically periodic with period two. A recent result of Sun and Xi is employed. Several examples...

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Bibliographic Details
Published inInternational journal of difference equations Vol. 4; no. 1; p. 43
Main Authors Berenhaut, Kenneth S, Guy, Richard T
Format Journal Article
LanguageEnglish
Published Research India Publications 01.06.2009
Subjects
Difference equations
Symmetric functions
United States
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ISSN0973-6069
0974-1828

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Summary:This paper introduces easily verified conditions which guarantee that all solutions to the equation [Y.sub.n] = f([Y.sub.n-k], [Y.sub.n-m]), with k,m [greater than or equal to] 1 and gcd(k,m) = 1 are asymptotically periodic with period two. A recent result of Sun and Xi is employed. Several examples are included. AMS Subject Classifications: 39A10, 39A11. Keywords: Difference equations, periodicity, symmetric functions, ratios, recursive equation.
ISSN:0973-6069
0974-1828