Oscillatory Properties of the Solutions of Nonlinear Delay Hyperbolic Differential Equations of Neutral Type

LIU An-ping; HE Meng-xing

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(6): 604-610

LIU An-ping, HE Meng-xing. Oscillatory Properties of the Solutions of Nonlinear Delay Hyperbolic Differential Equations of Neutral Type[J]. Applied Mathematics and Mechanics, 2002, 23(6): 604-610.

Citation:

LIU An-ping, HE Meng-xing. Oscillatory Properties of the Solutions of Nonlinear Delay Hyperbolic Differential Equations of Neutral Type[J]. Applied Mathematics and Mechanics, 2002, 23(6): 604-610.

Citation:

LIU An-ping, HE Meng-xing. Oscillatory Properties of the Solutions of Nonlinear Delay Hyperbolic Differential Equations of Neutral Type[J]. Applied Mathematics and Mechanics, 2002, 23(6): 604-610.

PDF( 272 KB)

Oscillatory Properties of the Solutions of Nonlinear Delay Hyperbolic Differential Equations of Neutral Type

LIU An-ping¹,
HE Meng-xing²

1.
Department of Mathematics and Physics, China University of Geosciences, Wuhan 430074, P R China;
2.
Department of Mathematics and Physics, Wuhan University of Technology, Wuhan 430070, P R China

Received Date: 2000-09-25
Rev Recd Date: 2001-12-26
Publish Date: 2002-06-15

Abstract

Abstract

By making use of the integral inequalities and some results of the functional differential equations,oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations of neutral type with multi-delays were investigated and a series of sufficient conditions for oscillations of the equations were established.The results fully indicate that the oscillations are caused by delay and hence reveal the difference between these equations and those equations without delay.
- neutral,
- delay,
- hyperbolic,
- oscillation,
- nonlinear

FullText(HTML)

References(15)

References

[1]	HE Meng-xing, GAO Shu-chun. Oscillations of hyperbolic functional differential equations with deviating argument[J]. Chinese Science Bulletin,1993,38(1):10-14.
[2]	刘安平. 含阻尼项非线性双曲型时滞偏微分方程解的振动性质[J]. 应用数学,1996,9(3):321-324.
[3]	刘安平. 中立双曲型时滞偏微分方程解振动的充要条件[J]. 工科数学,1997,13(3):40-42.
[4]	Mishev D P, Bainov D D. Oscillatory properties of the solutions of parabolic differential equations of neutral type[J]. Appl Math Comput,1988,28(1):97-111.
[5]	Yosida N. On the zeros of solutions of hyperbolic differential equations of neutral type[J]. Differential Intergral Equations,1990,3(2):155-160.
[6]	刘安平. 非线性抛物型时滞微分方程解的振动性质[J]. 东南大学学报,1999,29(3A):42-44.
[7]	刘安平,欧卓玲. 中立双曲型时滞微分方程解振动的充要条件[J]. 武汉工业大学学报,2000,22(2):89-91.
[8]	LIU An-ping. Necessary and sufficient conditions for oscillations of hyperbolic neutral partial differential equations[A]. In: Zhang J H, Zhang X N Eds. Proceedings of Interl Conf on Advanced Problems in Vibration Theory and Applications[C]. Beijing: Science Press,2000,740-742.
[9]	刘安平. 非线性中立双曲型微分方程解的振动判据[J]. 数学季刊,2001,16(4):6-12.
[10]	刘安平. 非线性中立抛物型泛函微分方程解的振动判据[J]. 应用泛函分析学报,2000,2(4):376-381.
[11]	CUI Bao-tong. Oscillatory properties of the solutions of hyperbolic differential equations with deviating argument[J]. Demonstratio Math,1996,29(1):61-68.
[12]	崔宝同,俞元洪,林诗仲,等. 具时滞双曲型微分方程解的振动性质[J]. 应用数学学报,1996,19(3):80-88.
[13]	Bainov D, CUI Bao-tong, Minchev E. Forced oscillatory properties of the solutions of hyperbolic differential equations of neutral type[J]. K Comput Appl Math,1996,72(4):309-318.
[14]	燕居让. n阶非线性时滞微分方程解的振动性与渐近性[J]. 数学学报,1990,33(4):537-542.
[15]	魏俊杰. 一阶偏差元微分方程振动的充要条件及其应用[J]. 数学学报,1989,32(5):632-638.