Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (4): 797-811.

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Oscillation of Second Order Nonlinear Differential Equations with Neutral Delay

Zhiyu Zhang1(),Yuanhong Yu2,Shuping Li3,Shizhu Qiao1   

  1. 1 Department of Sciences, Taiyuan Institute of Technology, Taiyuan 030008
    2 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190
    3 Department of Mathematics, North University of China, Taiyuan 030051
  • Received:2017-08-15 Online:2019-08-26 Published:2019-09-11
  • Supported by:
    the NSFC(11701528);the NSFC(11647034);the Natural Science Foundation of Shanxi Province(2011011002-3)


In this paper, the oscillatory behavior of solutions to a nonlinear second-order neutral differential equation is to study. Using double Riccati transformation and the technique of inequations, some new sufficient conditions are obtained for the solutions of all oscillations and the results generalize, improve and unify the oscillation theorems of half linear functional differential equations, nonlinear equations and generalized Emden-Fowler type equations in the literature recently. At last, some examples are given to illustrate the effectiveness of our results.

Key words: Second order nonlinear differential equation, Half linear differential equation, Emden-Fowler equation, Neutral, Riccati transformation, Oscillation criterion

CLC Number: 

  • O175