Existence of a Period-Two Solution in Linearizable Difference Equations
Consider the difference equation xn+1=f(xn,…,xn−k),n=0,1,…, where k∈{1,2,…} and the initial conditions are real numbers. We investigate the existence and nonexistence of the minimal period-two solution of this equation when it can be rewritten as the nonautonomous linear equation xn+l=∑i=1−lkgixn−i,...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/421545 |
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| Summary: | Consider the difference equation xn+1=f(xn,…,xn−k),n=0,1,…, where k∈{1,2,…} and the initial conditions are real numbers. We investigate the existence and nonexistence of the minimal period-two solution of this equation when it can be rewritten as the nonautonomous linear equation xn+l=∑i=1−lkgixn−i, n=0,1,…, where l,k∈{1,2,…} and the functions gi:ℝk+l→ℝ. We give some necessary and sufficient conditions for the equation to have a minimal period-two solution when l=1. |
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| ISSN: | 1026-0226 1607-887X |