On the Asymptotic Behavior of a Difference Equation with Maximum
We study the asymptotic behavior of positive solutions to the difference equation xn=max{A/xn-1α,B/xn−2β}, n=0,1,…, where 0<α, β<1, A,B>0. We prove that every positive solution to this equation converges to x∗=max{A1/(α+1),B1/(β+1)}.
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2008-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/243291 |
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| _version_ | 1832551078515703808 |
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| author | Fangkuan Sun |
| author_facet | Fangkuan Sun |
| author_sort | Fangkuan Sun |
| collection | DOAJ |
| description | We study the asymptotic behavior of positive solutions to the difference equation xn=max{A/xn-1α,B/xn−2β}, n=0,1,…, where 0<α, β<1, A,B>0. We prove that every positive solution to this equation converges to x∗=max{A1/(α+1),B1/(β+1)}. |
| format | Article |
| id | doaj-art-c853a2ce87e04db6999b600d24fc05d7 |
| 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-c853a2ce87e04db6999b600d24fc05d72025-02-03T06:05:07ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/243291243291On the Asymptotic Behavior of a Difference Equation with MaximumFangkuan Sun0College of Computer Science, Chongqing University, Chongqing 400044, ChinaWe study the asymptotic behavior of positive solutions to the difference equation xn=max{A/xn-1α,B/xn−2β}, n=0,1,…, where 0<α, β<1, A,B>0. We prove that every positive solution to this equation converges to x∗=max{A1/(α+1),B1/(β+1)}.http://dx.doi.org/10.1155/2008/243291 |
| spellingShingle | Fangkuan Sun On the Asymptotic Behavior of a Difference Equation with Maximum Discrete Dynamics in Nature and Society |
| title | On the Asymptotic Behavior of a Difference Equation with Maximum |
| title_full | On the Asymptotic Behavior of a Difference Equation with Maximum |
| title_fullStr | On the Asymptotic Behavior of a Difference Equation with Maximum |
| title_full_unstemmed | On the Asymptotic Behavior of a Difference Equation with Maximum |
| title_short | On the Asymptotic Behavior of a Difference Equation with Maximum |
| title_sort | on the asymptotic behavior of a difference equation with maximum |
| url | http://dx.doi.org/10.1155/2008/243291 |
| work_keys_str_mv | AT fangkuansun ontheasymptoticbehaviorofadifferenceequationwithmaximum |