Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 839-850.

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Oscillation of Second-Order Nonlinear Nonautonomous Delay Dynamic Equations on Time Scales

Ping Zhang1(),Jiashan Yang2(),Guijiang Qin2,*()   

  1. 1 School of Science, Shaoyang University, Hunan Shaoyang 422004
    2 School of Data Science and Software Engineering, Wuzhou University, Guangxi Wuzhou 543002
  • Received:2021-06-26 Online:2022-06-26 Published:2022-05-09
  • Contact: Guijiang Qin;;
  • Supported by:
    the NSFC(51765060);the Science Project of Hunan Province Education Department(20C1683);the NSF of Guangxi(2020JJA110021);the Basic Ability Improvement Project of Young and Middle-aged Teachers in Guangxi Universities(2020KY17007);the Key Project of Wuzhou University(2020B005);The Science and Technology Project of Shaoyang City(2021005ZD)


The oscillatory behavior of a class of second-order nonlinear nonautonomous variable delay damped dynamic equations are studied on a time scale T, where the equations are noncanonical form. By using the generalized Riccati transformation, and the time scales theory and the classical inequality, we establish some new oscillation criteria for the equation. The results fully reflect the influential actions of delay functions and damping terms in system oscillation. Finally, some examples are given to show that our results extend, improve and enrich those reported in the literature, and that they have good effectiveness and practicability.

Key words: Oscillation, Time scales, Emden-Fowler dynamic equations, Riccati transformation

CLC Number: 

  • O175.1