On the Periodicity of a Difference Equation with Maximum
We investigate the periodic nature of solutions of the max difference equation xn+1=max{xn,A}/(xnxn−1), n=0,1,…, where A is a positive real parameter, and the initial conditions x−1=Ar−1 and x0=Ar0 such that r−1 and r0 are positive rational numbers. The results in this paper answer the Open Problem...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/820629 |
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| _version_ | 1832558216973647872 |
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| author | Ali Gelisken Cengiz Cinar Ibrahim Yalcinkaya |
| author_facet | Ali Gelisken Cengiz Cinar Ibrahim Yalcinkaya |
| author_sort | Ali Gelisken |
| collection | DOAJ |
| description | We investigate the periodic nature of solutions of the max difference equation xn+1=max{xn,A}/(xnxn−1), n=0,1,…, where A is a positive real parameter, and the initial conditions x−1=Ar−1 and x0=Ar0 such that r−1 and r0 are positive rational numbers. The results in this paper answer the Open Problem 6.2 posed by Grove and Ladas (2005). |
| format | Article |
| id | doaj-art-fa2ca7dad153495e998dbf8932bc889a |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-fa2ca7dad153495e998dbf8932bc889a2025-02-03T01:33:04ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/820629820629On the Periodicity of a Difference Equation with MaximumAli Gelisken0Cengiz Cinar1Ibrahim Yalcinkaya2Department of Mathematics, Education Faculty, Selcuk University, 42099 Konya, TurkeyDepartment of Mathematics, Education Faculty, Selcuk University, 42099 Konya, TurkeyDepartment of Mathematics, Education Faculty, Selcuk University, 42099 Konya, TurkeyWe investigate the periodic nature of solutions of the max difference equation xn+1=max{xn,A}/(xnxn−1), n=0,1,…, where A is a positive real parameter, and the initial conditions x−1=Ar−1 and x0=Ar0 such that r−1 and r0 are positive rational numbers. The results in this paper answer the Open Problem 6.2 posed by Grove and Ladas (2005).http://dx.doi.org/10.1155/2008/820629 |
| spellingShingle | Ali Gelisken Cengiz Cinar Ibrahim Yalcinkaya On the Periodicity of a Difference Equation with Maximum Discrete Dynamics in Nature and Society |
| title | On the Periodicity of a Difference Equation with Maximum |
| title_full | On the Periodicity of a Difference Equation with Maximum |
| title_fullStr | On the Periodicity of a Difference Equation with Maximum |
| title_full_unstemmed | On the Periodicity of a Difference Equation with Maximum |
| title_short | On the Periodicity of a Difference Equation with Maximum |
| title_sort | on the periodicity of a difference equation with maximum |
| url | http://dx.doi.org/10.1155/2008/820629 |
| work_keys_str_mv | AT aligelisken ontheperiodicityofadifferenceequationwithmaximum AT cengizcinar ontheperiodicityofadifferenceequationwithmaximum AT ibrahimyalcinkaya ontheperiodicityofadifferenceequationwithmaximum |