| Ethiraju Thandapani,刘召爽,李巧銮,Sebastian Elizabeth.含最大值项二阶中立型差分方程的渐近性[J].数学研究及应用,2006,26(2):191~198 |
| 含最大值项二阶中立型差分方程的渐近性 |
| Asymptotic Behavior of Second Order Neutral Difference Equations with Maxima |
| 投稿时间：2004-07-15 |
| DOI：10.3770/j.issn:1000-341X.2006.02.001 |
| 中文关键词: 渐近性 非振动 中立型差分方程 最大值. |
| 英文关键词:asymptotic behavior nonoscillation neutral difference equation maxima. |
| 基金项目:河北省自然科学基金 (103141); 河北师范大学重点科学基金 (1301808) |
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| 中文摘要: |
| 考虑含最大值项二阶中立型差分方程$$\Delta \left( {a_n \Delta \left( {y_n + p_n y_{n-k}} \right)}\right) - q_n \mathop {\max }\limits_{[n - \ell ,n]} y_s = 0,\quad n = 0,1,2, \cdots ,\eqno{(*)}$$其中 $\left\{ {a_n } \right\},\left\{ {p_n } \right\}$和$\left\{ {q_n } \right\}$ 为实数列, $k$和$\ell$ 为整数且 $k\ge 1$ , $\ell\ge 0$, 我们研究了方程$(*)$非振动解的渐近性. 通过例子说明了含最大值项的方程和相应的不含最大值项方程之间的区别. |
| 英文摘要: |
| 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. |
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