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 |
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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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| author | E. J. Janowski M. R. S. Kulenović |
| author_facet | E. J. Janowski M. R. S. Kulenović |
| author_sort | E. J. Janowski |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-281f86c4d29448ccbc2acb4b4151b0f3 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-281f86c4d29448ccbc2acb4b4151b0f32025-08-20T03:54:42ZengWileyDiscrete 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 |
| spellingShingle | E. J. Janowski M. R. S. Kulenović Existence of a Period-Two Solution in Linearizable Difference Equations Discrete Dynamics in Nature and Society |
| title | 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_short | Existence of a Period-Two Solution in Linearizable Difference Equations |
| title_sort | existence of a period two solution in linearizable difference equations |
| url | http://dx.doi.org/10.1155/2013/421545 |
| work_keys_str_mv | AT ejjanowski existenceofaperiodtwosolutioninlinearizabledifferenceequations AT mrskulenovic existenceofaperiodtwosolutioninlinearizabledifferenceequations |