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数学与物理学

具连续偏差变元的二阶阻尼微分方程的振动性

  • 林文贤
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  • 韩山师范学院数学与应用数学系, 广东 潮州 521041

收稿日期: 2011-04-25

  修回日期: 2011-06-27

  网络出版日期: 2012-09-15

Oscillation for certain second-order damped differential equations with continuous deviating arguments

  • LIN Wen-Xian
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  • Department of Mathematics and Applied Mathematics, Hanshan Normal University, Chaozhou 521041, Guangdong, China

Received date: 2011-04-25

  Revised date: 2011-06-27

  Online published: 2012-09-15

摘要

获得一类具有连续偏差变元的非线性二阶阻尼泛函微分方程所有解振动的若干充分条件. 所得结果包含和推广了已有文献中的相关结论,并给出2个应用实例.

本文引用格式

林文贤 . 具连续偏差变元的二阶阻尼微分方程的振动性[J]. 中国科学院大学学报, 2012 , 29(5) : 594 -598 . DOI: 10.7523/j.issn.2095-6134.2012.5.003

Abstract

We obtain sufficient conditions for the oscillation of all solutions of the nonlinear second-order damped functional differential equations with continuous deviating arguments. This work generalizes and improves some known results. The main results are illustrated by two examples.

参考文献

[1] Kong Q. Interval criteria for oscillation of second order linear equations[J]. J Math Anal Appl, 1999,229: 258-270.
[2] Philos C G. Oscillation theorems for linear differential equations of second order[J]. Arch Math(Besel), 1989, 53: 482-492.
[3] Li W T, Agarwal R P. Interval oscillation criteria related to integral averaging technique for certain nonlinear differential equations[J]. J Math Anal Appl, 2000, 245: 171-178.
[4] Li W T, Agarwal R P. Interval oscillation criteria for second order nonlinear differential equations with damping[J]. Computer Math Appl, 2000, 40: 217-230.
[5] Shi W Y, Zhao X S, Dai X D. Oscillation theorems for second-order damped differential equations with distributed deviating arguments[J]. Journal of Hebei University:Natural Science Edition, 2007, 7(4): 340-344(in Chinese). 师文英,赵新生,戴晓东. 具有连续偏差变元的二阶阻尼方程的振动定理[J]. 河北大学学报:自然科学版, 2007, 27(4): 340-344.
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