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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| Format: | Article |
| Language: | English |
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Hindawi Limited
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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doaj-281f86c4d29448ccbc2acb4b4151b0f32020-11-25T00:51:45ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/421545421545Existence of a Period-Two Solution in Linearizable Difference EquationsE. J. Janowski0M. R. S. Kulenović1Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USADepartment of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USAConsider 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.http://dx.doi.org/10.1155/2013/421545 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
E. J. Janowski M. R. S. Kulenović |
| spellingShingle |
E. J. Janowski M. R. S. Kulenović Existence of a Period-Two Solution in Linearizable Difference Equations Discrete Dynamics in Nature and Society |
| author_facet |
E. J. Janowski M. R. S. Kulenović |
| author_sort |
E. J. Janowski |
| title |
Existence of a Period-Two Solution in Linearizable Difference Equations |
| title_short |
Existence of a Period-Two Solution in Linearizable Difference Equations |
| title_full |
Existence of a Period-Two Solution in Linearizable Difference Equations |
| title_fullStr |
Existence of a Period-Two Solution in Linearizable Difference Equations |
| title_full_unstemmed |
Existence of a Period-Two Solution in Linearizable Difference Equations |
| title_sort |
existence of a period-two solution in linearizable difference equations |
| publisher |
Hindawi Limited |
| series |
Discrete Dynamics in Nature and Society |
| issn |
1026-0226 1607-887X |
| publishDate |
2013-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2013/421545 |
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AT ejjanowski existenceofaperiodtwosolutioninlinearizabledifferenceequations AT mrskulenovic existenceofaperiodtwosolutioninlinearizabledifferenceequations |
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