Acta mathematica scientia,Series A ›› 2018, Vol. 38 ›› Issue (1): 134-155.

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Oscillation for a Class of Second-Order Damped Emden-Fowler Dynamic Equations on Time Scales

Yang Jiashan1,2, Li Tongxing3   

  1. 1. School of Information and Electronic Engineering, Wuzhou University, Guangxi Wuzhou 543002;
    2. Laboratory of Complex System Simulation and Intelligent Computing, Wuzhou University, Guangxi Wuzhou 543002;
    3. School of Informatics, Linyi University, Shandong Linyi 276005
  • Received:2016-12-02 Revised:2017-04-06 Online:2018-02-26 Published:2018-02-26
  • Supported by:
    Supported by the NSFC (61503171, 61403061, 11447005), the Scientific Research Fund of Education Department of Guangxi Zhuang Autonomous Region (2013YB223) and the Master's Degree Awards Unit Project Construction Project (GUI Degree[2013]4)

Abstract: The oscillation for certain second-order nonlinear neutral variable delay Emden-Fowler dynamic equations with damping on time scales is discussed. By using the time scales theory and the generalized Riccati transformation and the inequality technique, we establish six new oscillation criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of second-order nonlinear damped Emden-Fowler differential equations and difference equations. Two examples are given to illustrate the main results of this article.

Key words: Oscillation, Neutral dynamic equations, Time scales, Damping term, Variable delay

CLC Number: 

  • O175.7
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