existence of a period-two solution in linearizable difference equations
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2013
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Abstract
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.
| Reference Key |
janowski2013discreteexistence
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|---|---|
| Authors | ;E. J. Janowski;M. R. S. Kulenović |
| Journal | Journal of the American Heart Association |
| Year | 2013 |
| DOI |
10.1155/2013/421545
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