某些四阶时滞微分方程解的稳定性

西密尔·通兹

某些四阶时滞微分方程解的稳定性

西密尔·通兹

玉珍翠延大学文学与科学学院数学系,凡城 65080 土耳其

详细信息

中图分类号: O357.3
计量
- 文章访问数: 2610
- HTML全文浏览量: 161
- PDF下载量: 876
- 被引次数: 0
出版历程
- 收稿日期: 2005-02-22
- 修回日期: 2005-08-18
- 刊出日期: 2006-08-15

On the Stability of Solutions of Certain Fourth-Order Delay Differential Equations

Cemil Tun

Department of Mathematics, Faculty of Arts and Sciences, Yüzüncü YⅡ University 65080, Van-Turkey

摘要

摘要: 利用Liapunov函数法，得到了一个新的、证明某些四阶非线性时滞微分方程零解渐近稳定的结果．建立结果的限制性条件弱于其他文献给出的的方法．
- 四阶非线性时滞微分方程 /
- 稳定性 /
- Liapunov泛函
Abstract: By the use of the Liapunov functional approach,a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay.The established result is less restrictive than those reported in the literature.
- non-linear delay differential equation of fourth order /
- stability /
- Liapunov functional

HTML全文

参考文献(30)

[1]	BereketoAglu H.Asymptotic stability in a fourth order delay differential equation[J].Dynam Systems Appl,1998,7(1):105—115.
[2]	Burton T A.Volterra Integral and Differential Equations[M].New York：Academic Press,1983.
[3]	Burton T A.Stability and Periodic Solutions of Ordinary and Functional Differential Equations[M].Orlando:Academic Press,1985.
[4]	Burton T A,Zhang S N.Unified boundedness, periodicity, and stability in ordinary and functional-differential equations[J].Ann Mat Pura Appl,1986,145(4):129—158. doi: 10.1007/BF01790540
[5]	Chukwu E N.On the boundedness and stability properties of solutions of some differential equations of the fifth order[J].Ann Mat Pura Appl,1975,106(4):245—258. doi: 10.1007/BF02415032
[6]	Chukwu E N.On the boundedness and stability of solutions of some differential equations of the fifth order[J].SIAM J Math Anal,1976,7(2),176—194.
[7]	Gopalsamy K.Stability and Oscillations in Delay Differential Equations of Population Dynamics[M].Dordrecht:Kluwer Academic Publishers Group,1992.[JP3]. Hale J.Theory of Functional Differential Equations[M].New York，Heidelberg:Springer-Verlag,1977.
[9]	Harrow M.A stability result for solutions of certain fourth order homogeneous differential equations[J].J London Math Soc,1967,42：51—56. doi: 10.1112/jlms/s1-42.1.51
[10]	Harrow M.On the boundedness and the stability of solutions of some differential equations of the fourth order[J].SIAM J Math Anal,1970,1：27—32. doi: 10.1137/0501002
[11]	Kolmanovskii V,Myshkis A.Introduction to the Theory and Applications of Functional Differential Equations[M].Dordrecht:Kluwer Academic Publishers,1999.
[12]	Ku Y H.Liapunov function of a sixth-order nonlinear system[J].Proc IEEE,1969,57:91—94.
[13]	Makay G.On the asymptotic stability of the solutions of functional-differential equations with infinite delay[J].J Differential Equations,1994,108(1)：139—151. doi: 10.1006/jdeq.1994.1029
[14]	Okoronkwo E O.On stability and boundedness of solutions of a certain fourth-order delay differential equation[J].Internat J Math Math Sci,1989,12(3)：589—602. doi: 10.1155/S0161171289000724
[15]	Qian C.On global stability of third-order nonlinear differential equations[J].Nonlinear Anal,Ser A:Theory Methods,2000,42(4):651—661. doi: 10.1016/S0362-546X(99)00120-0
[16]	Reissig R,Sansone G,Conti R.Non-linear Differential Equations of Higher Order[M].Leyden:Noordhoff International Publishing,1974.
[17]	Sadek A I.Stability and boundedness of a kind of third-order delay differential system[J].Applied Mathematics Letters,2003,16(5)：657—662. doi: 10.1016/S0893-9659(03)00063-6
[18]	Sadek A I.On the stability of solutions of certain fourth order delay differential equations[J].Applied Mathematics and Computation,2004,148(2)：587—597. doi: 10.1016/S0096-3003(02)00925-6
[19]	LI Sen-lin,WEN Li-zhi.Functional Differential Equations[M].Changsha:Hunan Science and Technology Press,1987.
[20]	Sinha A S C.Stability result of a sixth order non-linear system[J].Automatica J,IFAC,1971,7:641—643. doi: 10.1016/0005-1098(71)90029-X
[21]	Sinha A S C.On stability of solutions of some third and fourth order delay-differential equations[J].Information and Control,1973,23：165—172. doi: 10.1016/S0019-9958(73)90651-7
[22]	Tejumola H O,Tchegnani B.Stability, boundedness and existence of periodic solutions of some third and fourth order nonlinear delay differential equations[J].J Nigerian Math Soc,2000,19:9—19.
[23]	Tun C.On the boundedness and the stability results for the solutions of certain fifth order differential equations[J].University of Istanbul,The Journal of Mathematics,1995,54:151—160.
[24]	Tun C.A study of the stability and boundedness of the solutions of nonlinear differential equations of the fifth order[J].Indian J Pure Appl Math,2002,33(4)：519—529.
[25]	Tun C.A note on the stability and boundedness results of solutions of certain fourth order differential equations[J].Applied Mathematics and Computation,2004,155(3)：837—843. doi: 10.1016/S0096-3003(03)00819-1
[26]	Tun C.Some stability results for the solutions of certain fourth order delay differential equations[J].Differential Equations and Applications,2004,4:165—174.
[27]	Tun C.Uniform ultimate boundedness of the solutions of third-order nonlinear differential equation[J].Kuwait Journal of Science and Engineering,2005,32(1)：1—10.
[28]	Tun C.New results about stability and boundedness of solutions of certain non-linear third-order delay differential equations[J].Arabian Journal for Science and Engineering, 2006,31(2A).(in press).
[29]	Yoshizawa T.Stability Theory by Liapunov's Second Method[M].Tokyo:The Mathematical Society of Japan,1966.
[30]	QIN Yuan-xun,LIU Yong-qing,WANG Lian.Stability of Motion for Dynamic Systems With Delay[M].Beijing:Academic Press,1966.
[31]	Zhu Y F.On stability, boundedness and existence of periodic solution of a kind of third order nonlinear delay differential system[J].Ann Differential Equations,1992,8(2)：249—259.