2008 / September Volume 3 No.3
Oscillatory and asymptotic behavior of a homogeneous neutral delay difference equation of second order
| Published Date |
2008 / September
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|---|---|
| Title | Oscillatory and asymptotic behavior of a homogeneous neutral delay difference equation of second order |
| Author | |
| Keyword | |
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| Pagination | 453-467 |
| Abstract | In this paper we find sufficient conditions for every solution of the neutral delay difference equation
$\Delta(r_n\Delta(y_n - p_ny_n - m))+ q_nG(y_{n-k}) = 0$ to oscillate or to tend to zero or $\pm\infty$ as $n \to \infty$, where $\Delta$ is the forward difference operator given by $\Delta x_n = x_{n+1}- x_n, p_n, q_n,$ and $r_n$ are infinite sequences of real numbers with $q_n \ge 0, r_n > 0$. Different ranges of {$p_n$} are considered. This paper improves, generalizes and corrects some recent results of [1, 9, 12, 13, 14]. |
| AMS Subject Classification |
39A10, 39A12
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| Received |
2007-08-11
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| Accepted |
2007-08-11
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