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二阶非线性阻尼方程的振动准则 被引量：10

Oscillation Criteria for Second Order Nonlinear Differential Equation With Damping
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摘要 　利用Riccati变换和积分平均方法,研究了一类具有阻尼项的二阶非线性方程的解为振动的若干充分条件,建立了一些判定上述方程为振动的充分准则。 By the generalized Riccati transformation and the integral averaging technique.Some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.
作者 罗辉 庄容坤 郭兴明
机构地区 惠州学院数学系 上海大学上海市应用数学和力学研究所
出处 《应用数学和力学》 EI CSCD 北大核心 2005年第4期403-410,共8页 Applied Mathematics and Mechanics
基金 广东省自然科学基金资助项目
关键词 二阶非线性阻尼方程 振动性 RICCATI变换 积分平均技巧 second order nonlinear differential equation with damping oscillation Riccati transformation integral averaging technique
分类号 O175 [理学—基础数学]
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参考文献9

  • 1王其如.二阶非线性微分方程的振动准则[J].数学学报（中文版）,2001,44(2):371-376. 被引量：45
  • 2Kirane M, Rogovchenko Yu V. Oscillation results for a second order damped differential equation with nonmonotonous nonlinearity[ J]. J Math Anal Appl,2000,250(1): 118-138.
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二级参考文献5

  • 1[1]Rogovchenko Y. V., Oscillation Criteria for Certain Nonlinear Differential Equations [J], J. Math. Anal.Appl., 1999, 229(2): 399-416.
  • 2[2]Hameclani G. G., Krenz G. S., Oscillation Criteria for Certain Second Order Differential Equations [J], J.Math. Anal. Appl., 1990, 149(1): 271-276.
  • 3[3]Grace S. R., Lalli B. S., An Oscillation Criterion for Certain Second Order Strongly Sublinear Differential Equations [J], J. Math. Anal. Appl., 1987, 123(2): 584-588.
  • 4[4]Philos Ch G., Oscillation Theorems for Linear Differential Equations of Second Order [J], Arch. Math.(Basel), 1989, 53(5): 482-492.
  • 5[5]Erbe L., Oscillation Criteria for Second Order Nonlinear Delay Equations [J], Canad Math. Bull., 1973,16(1): 49-56.

共引文献44

同被引文献69

引证文献10

二级引证文献33

应用数学和力学
2005年 第4期

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