| Asymptotic Behavior of Second Order Neutral Difference Equations with Maxima |
| Received:July 15, 2004 |
| Key Words:
asymptotic behavior nonoscillation neutral difference equation maxima.
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| Fund Project:the Natural Science Foundation of Hebei Province (103141); Key Science Foundation of Hebei Normal University (1301808) |
| Author Name | Affiliation | | Ethiraju Thandapani | Dept. of Math., Periyar University, Salem-636011, Tamilnadu, India | | LIU Zhao-shuang | College of Math. & Phys., Shijiazhuang University of Economics, Hebei 050031, China
College of Math. & Info. Sci., Hebei Normal University, Shijiazhuang 050016, China | | LI Qiao-luan | College of Math. & Info. Sci., Hebei Normal University, Shijiazhuang 050016, China | | Sebastian Elizabeth | Dept. of Math., Periyar University, Salem-636011, Tamilnadu, India |
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| Abstract: |
| The authors consider the following second order neutral difference equation with maxima $$\Delta ( {a_n \Delta ( {y_n + p_n y_{n-k}} )}) - q_n\max_{[n - \ell ,n]} y_s = 0,\quad n = 0,1,2, \cdots ,\eqno{(*)}$$ where $\{ {a_n } \},\{ {p_n } \}$ and $\{ {q_n } \}$ are sequences of real numbers, and $k$ and $\ell$ are integers with $k\ge 1$ and $\ell\ge 0$. And the asymptotic behavior of nonoscillatory solutions of $(*)$. An example is given to show the difference between the equations with and without ``maxima" is studied. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2006.02.001 |
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