| 二阶线性矩阵微分系统的振动性 |
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| 引用本文： | 郑召文,孟凡伟,俞元洪.二阶线性矩阵微分系统的振动性[J].数学学报,1998,41(6):0-1238. |
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| 作者姓名： | 郑召文 孟凡伟 俞元洪 |
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| 作者单位： | [1]曲阜师范大学数学系 [2]中科院应用数学研究所 |
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| 基金项目： | 国家自然科学基金，山东省青年自然科学基金 |
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| 摘 要： | 本文研究了矩阵微分系统（P（t）Y′）′＋Q（t）Y＝0，t∈［t0，∞）．其中P，Q和Y是n×n实连续矩阵函数，且P（t）和Q（t）是对称的．P（t）是正定矩阵（P（t）＞0，t∈［t0，∞））．利用推广的Riccati变换，得到了系统（1）振动的若干新判据．所得结果改进了Erbe，Kong和Ruan的相应结果．
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| 关 键 词： | 矩阵微分系统 振动 Riccati变换 |
On the Oscillation of Second Order Linear Matrix Differential Systems |
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| Zheng Zhaowen, Meng Fanwei.On the Oscillation of Second Order Linear Matrix Differential Systems[J].Acta Mathematica Sinica,1998,41(6):0-1238. |
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| Authors: | Zheng Zhaowen Meng Fanwei |
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| Institution: | Zheng Zhaowen; Meng Fanwei (Department of Mathematics, Qufu Normal University, Qufu 273165, China) Yu Yuanhong (Institute of Applied Mathematics, Academic Sinica, Beijing 100080, China) |
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| Abstract: | In the present paper matrix differential system of the form (P(t)Y')' + Q(t)Y = 0, t ∈ t0, ∞) is considered, where P,Q and Y are n x n real continuous matrix functions, p(t) and Q(t) are symmetric, and p(t) > 0, t ∈ t0,∞). Using Riccati transformation generalized some new oscillation criteria for the system are established. The criteria obtained improve Erbe, Kong and Ruan's results in 4]. |
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| Keywords: | Matrix differential system Oscillation Riccati transformation |
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