三阶非线性时滞微分方程振动性的新准则

罗李平; 俞元洪; 曾云辉

doi:10.3879/j.issn.1000-0887.2013.09.007

三阶非线性时滞微分方程振动性的新准则

doi: 10.3879/j.issn.1000-0887.2013.09.007

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

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)

详细信息

作者简介:
罗李平(1964—), 教授(通讯作者.E-mail: luolp3456034@163.com);俞元洪（1939—），男，研究员，硕士(E-mail: yu84845366@126.com);曾云辉（1978—），男，讲师，硕士(E-mail: chj8121912@sina.com).

中图分类号: O175.12
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出版历程
- 收稿日期: 2013-05-27
- 修回日期: 2013-06-11
- 刊出日期: 2013-09-15

New Criteria for Oscillation of Third Order Nonlinear Delay Differential Equations

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

摘要

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.
- 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
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.
- variational third order /
- delay differential equation /
- A-type solution /
- B-type solution /
- comparison theorem /
- oscillation criterion /
- nonlinear

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参考文献(15)

[1]	Schot S H. Jerk: the time rate of change of acceleration[J]. Am J Phys,1978,46(11): 1090-1094.
[2]	罗李平, 俞元洪.三阶半线性中立型微分方程的振动结果[J].系统科学与数学, 2012,32(5): 571-579.(LUO Li-ping, YU Yuan-hong. Oscillation results of third order half linear neutral differential equations[J]. J Sys Sci & Math Scis,2012,32(5): 571-579. (in Chinese))
[3]	Aktas M F, Tiryaki A, Zafer A. Oscillation criteria for third order nonlinear functional differential equations[J].Appl Math Letters,2010, 23(7): 756-762.
[4]	Aktas M F, Tiryaki A, Zafer A. Integral criteria for oscillation of third order nonlinear differential equations[J].Nonl Anal,2009,71(12): 1496-1502.
[5]	Grace S R, Agarwal R P, Pavani R, Thandapani E. On the oscillation of certain third order nonlinear functional differential equations[J].Appl Math Comput,2008, 202(1): 102-112.
[6]	Grace S R, Agarwal R P , Aktas M F. On the oscillation of third order functional differential equations[J].Indian J Pure Appl Math,2008,39: 491-507.
[7]	Tiryaki A, Aktas M F. Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping[J].J Math Anal Appl,2007, 325(1): 54-68.
[8]	Saker S H. Oscillation criteria of third order nonlinear delay differential equations[J]. Math Slovaca,2006, 56(4): 433-450.
[9]	Li T, Thandapani E. Oscillation of solutions to oddorder nonlinear neutral functional differential equations[J]. Electron J Diff Equs,2011, 2011(23): 1-12.
[10]	Liu Z, Chen L, Kang S M, Cho S Y. Existence of nonoscillatory solutions for a thirdorder nonlinear neutral delay differential equation[J]. Abstract and Applied Analysis ,Vol 2011, Article ID 693890, 23 pages, 2011.doi: 10.1155/2011/693890.
[11]	Thandapani E, Li T. On the oscillation of third order quasilinear neutral functional differential equations[J]. Archivum Mathematicum,2011,47(3): 181-199.
[12]	Baculíkov B, Durina J. Oscillation of thirdorder functional differential equations[J]. EJQTDE,2010(43): 1-10.
[13]	Baculíkov B, Durina J. Oscillation of thirdorder nonlinear differential equations[J]. Appl Math Letters,2011,24(4): 466-470.
[14]	高正晖, 罗李平. 含分布时滞与阻尼项的三阶非线性微分方程的 Philos 型振动[J]. 山东大学学报(理学版), 2013, 48(4): 85-90.(GAO Zheng-hui, LUO Li-ping. Philos-type oscillation criteria for thirdorder nonlinear functional differential equations with distributed delays and damped terms[J]. Journal of Shandong University(Natural Science),2013,48(4): 85-90.(in Chinese))
[15]	Philos Ch G. On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delays[J]. Archivum Mathematicum,1981,36(1): 168-178.

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三阶非线性时滞微分方程振动性的新准则

doi: 10.3879/j.issn.1000-0887.2013.09.007

作者简介:
罗李平(1964—), 教授(通讯作者.E-mail: luolp3456034@163.com);俞元洪（1939—），男，研究员，硕士(E-mail: yu84845366@126.com);曾云辉（1978—），男，讲师，硕士(E-mail: chj8121912@sina.com).

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New Criteria for Oscillation of Third Order Nonlinear Delay Differential Equations

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留言板

三阶非线性时滞微分方程振动性的新准则

doi: 10.3879/j.issn.1000-0887.2013.09.007

作者简介: 罗李平(1964—), 教授(通讯作者.E-mail: luolp3456034@163.com);俞元洪（1939—），男，研究员，硕士(E-mail: yu84845366@126.com);曾云辉（1978—），男，讲师，硕士(E-mail: chj8121912@sina.com).

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出版历程

New Criteria for Oscillation of Third Order Nonlinear Delay Differential Equations

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出版历程

目录

作者简介:
罗李平(1964—), 教授(通讯作者.E-mail: luolp3456034@163.com);俞元洪（1939—），男，研究员，硕士(E-mail: yu84845366@126.com);曾云辉（1978—），男，讲师，硕士(E-mail: chj8121912@sina.com).