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具分布时滞和阻尼项的偶阶半线性中立型微分方程的振动性 被引量：2

OSCILLATION OF EVEN-ORDER HALF-LINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH DISTRIBUTED DELAY AND DAMPING TERM
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摘要 研究一类具分布时滞和阻尼项的偶阶半线性中立型微分方程解的振动性质,利用广义Riccati变换和积分平均技巧得到方程一切解均为振动的若干新的振动准则,推广、改进和统一了新近文献中的某些结果. In this paper,we are concerned with a class of even-order half-linear neutral differential equations with distributed delay and damping term.By using the generalized Riccati technique and the integral averaging technique,new oscillation criteria are obtained for every solution of the equations to be oscillatory,which extend, improve and unify some known results in the literature recently.
作者 高丽 张全信 俞元洪
机构地区 滨州学院数学与信息科学系 中国科学院数学与系统科学研究院
出处 《系统科学与数学》 CSCD 北大核心 2013年第5期568-578,共11页 Journal of Systems Science and Mathematical Sciences
基金 山东省自然科学基金(ZR2010AM031 ZR2011AL011) 山东省科技发展计划(2010GWZ20401)资助项目
关键词 振动准则 阻尼 半线性 分布时滞 积分平均方法 Oscillation criterion damping half-linear distributed delay integral averaging method
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献14

  • 1Meng F W, Xu R. Oscillation criteria for certain even order quasi-linear neutral differential equations with deviating arguments. Appl. Math. Comput., 2007, 190(1): 458-464.
  • 2Agarwal R P, Grace S R, O'Regan D. Oscillation criteria for certain nth order differential equa- tions with deviating arguments. J. Math. Anal. Appl., 2001, 262(2): 601-622.
  • 3Li H J. Oscillation criteria for half-linear second order differential equations. Hiroshima Math. J., 1995, 25(3): 571-583.
  • 4Liu S H, Zhang Q X, Yu Y H. Oscillation of even order half-linear functional differential equations with damping. Comput. Math. Appl., 2011, 61(8): 2191-2196.
  • 5Meng F W, Xu R. Kamenev-type oscillation criteria for even order neutral differential equations with deviating arguments. Appl. Math. Comput., 2007, 190(2): 1402-1408.
  • 6Wang Q R. Oscillation and asymptotics for second-order half-linear differential equations. Appl. Math. Comput., 2001, 122(2): 253-266.
  • 7Wang P G. Oscillation criteria for second-order neutral equations with distributed deviating arguments. Comput. Math. Appl., 2004, 47(12): 1935-1946.
  • 8Wang P G, Teo K L, Liu Y Q. Oscillation properties for even order neutral equations with distributed deviating arguments. J. Comput. Appl. Math., 2005, 182(2): 290-303.
  • 9Xu Z T. Kamenev-type oscillation criteria for even order delay differential equations. Utilitas Math., 2009, 78: 65-77.
  • 10Xu Z T, Xia Y. Integral averaging technique and oscillation of certain even order delay differential equations. J. Math. Anal. Appl., 2004, 292(1): 238-246.

二级参考文献15

  • 1Wintner A. A Criterion of Oscillatory Stability. Quart. Appl. Math., 1949, 7:115-117.
  • 2Kanenev I V. An Integral Criterion for Oscillation of Linear Differential Equations of Second Order. Math. Zametki, 1978, 23:249-251.
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  • 4Philos Ch G. Oscillation Theorems for Linear Differential Equations of Second Order. Arch. Math., 1989, 53:482 -492.
  • 5Li H J. Oscillation Criteria for Half-linear Second Order Differential Equations. Hiroshima Math. J., 1995, 25:571-583.
  • 6Wang P G, Teo K L, Liu Y Q. Oscillation Properties for Even order Neutral Equations with Distributed Deviating Arguments. J. Comput. Appl. Math., 2005, 182:290-303.
  • 7Agarwal R P, Grace S R, O'Regan D. Oscillation Criteria for Certain rtth Order Differential Equations with Deviating Arguments. J. Math. Anal. Appl., 2001, 262:601-622.
  • 8Dosly O, Lomtatidze A. Oscillation and Nonoscillation Criteria for Half-linear Second Order Differ- ential Equations. Hiroshima Math. J., 2006, 36:203-219.
  • 9Hsu H B, Yeh C C. Oscillation Theorems for Second-order Half-linear Differential Equations. AppL Math. Lett., 1999, 9:71-77.
  • 10Wang Q R. Oscillation and Asymptotics for Second-order Half-linear Differential Equations. Appl. Math. Comput,, 2001, 122:253-266.

共引文献13

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系统科学与数学
2013年 第5期

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