| 三阶非线性时滞微分方程振动性的新准则 |
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| 引用本文： | 罗李平,俞元洪,曾云辉.三阶非线性时滞微分方程振动性的新准则[J].应用数学和力学,2013,34(9):941-947. |
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| 作者姓名： | 罗李平 俞元洪 曾云辉 |
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| 作者单位： | 1衡阳师范学院 数学与计算科学系, 湖南 衡阳 421002;2中国科学院 数学与系统科学研究院, 北京 100190 |
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| 基金项目： | 湖南省自然科学-衡阳联合基金资助项目(11JJ9002); 湖南省“十二五”重点建设学科资助项目(湘教发[2011]76号) |
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| 摘 要： | 研究了一类三阶非线性时滞微分方程的振动性问题, 利用算子和积分技巧给出了该类方程不存在A型解(或B型解)的判定条件．进而借助适当的比较定理, 得到了该类方程振动的几个新的充分条件, 所得结果推广和改进了最近文献中的结果, 并充分反映了时滞在方程振动中的影响作用．主要结果由实例加以阐述.
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| 关 键 词： | 三阶 时滞微分方程 A型解 B型解 比较定理 振动准则 非线性 |
| 收稿时间： | 2013-05-27 |
New Criteria for Oscillation of Third Order Nonlinear Delay Differential Equations |
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| Institution: | 1Department of Mathematics and Computational Science, Hengyang Normal University, Hengyang, Hunan 421002, P.R.China;2Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R.China |
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| Abstract: | Oscillatory problems of a class of third order nonlinear delay differential equations were studied. With the techniques of operator and integral, the determinant conditions in which such equations had not A-type solution (or B-type solution) were given. Further, several new sufficient conditions for oscillation of such equations were obtained via suitable comparison theorems. Obtained results generalize and improve some known results of the latest literature and fully reflect the influence action of delay in equation oscillation. The main results are illustrated by some examples. |
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