| 一类时滞微分方程解的振动准则 |
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| 引用本文： | 何利平.一类时滞微分方程解的振动准则[J].晋城职业技术学院学报,2011,4(5):73-75. |
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| 作者姓名： | 何利平 |
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| 作者单位： | 晋城职业技术学院,山西晋城,048026 |
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| 摘 要： | 考虑一类具有正负系数的时滞微分方程x（＇t）＋1tlntni=1Σpix（tα）i-1tlntni=1Σqix（tβ）i=0,其中0〈αi〈1,0〈βi〈1,pi〉0,qi≥0是常数,证明了方程所有解振动的一个充分条件为αi〈βi,ni=1Σpi〉ni=1Σqi,ni=1Σqilnβiα≤1,ni=1Σ（pi-qi）ln1α〉1e其中α=max{α1,α2,…,αn≤≤}.
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| 关 键 词： | 时滞微分方程 振动 正负系数 |
Oscillation Criteria for Delay Differential Equations with Positive and Negative Coefficients |
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| HE Li-ping.Oscillation Criteria for Delay Differential Equations with Positive and Negative Coefficients[J].Journal of Jincheng Institute of Technology,2011,4(5):73-75. |
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| Authors: | HE Li-ping |
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| Institution: | HE Li-ping(Jincheng Institute of Technology,Jincheng,Shanxi 048026,China) |
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| Abstract: | Consider the delay differential equation with positive and negative coefficients x＇（t）＋ 1 tlnt i = 1 Σp i x（t α）i 1 tlnt i = 1 Σq i x（t β）i =0,where0α i 1,0β i 1,p i 0andq i ≥0 are constants.It is proved that a sufficient condition of oscillation of all solutions of the equation isα i β i,n Σp i n Σq i,n Σq i ln β i α ≤1,n Σ（pi-q）iln 1 α 1 e whereα=max{α 1,α 2,…,α n ≤ Σ}. |
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| Keywords: | delay differential equations oscillation positive and negative coefficients |
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