Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1492-1503.

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Oscillation Theorems of Second-Order Variable Delay Dynamic Equations with Quasilinear Neutral Term

Guijiang Qin1,2(),Jiashan Yang1,3,*()   

  1. 1 School of Data Science and Software Engineering, Wuzhou University, Guangxi Wuzhou 543002
    2 Guangxi Colleges and Universities Key Laboratory of Professional Software Technology, Wuzhou University, Guangxi Wuzhou 543002
    3 Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System, Wuzhou University, Guangxi Wuzhou 543002
  • Received:2021-01-18 Online:2021-10-26 Published:2021-10-08
  • Contact: Jiashan Yang E-mail:57841824@qq.com;syxyyjs@163.com
  • Supported by:
    the NSFC(51765060);the NSF of Guangxi(2018JJB170034);the Basic Ability Improvement Project of Young and Middle-aged Teachers in Guangxi Universities(2018KY0543);the Basic Ability Improvement Project of Young and Middle-aged Teachers in Guangxi Universities(2020KY17007);the Key Project of Wuzhou University(2016B008);the Key Project of Wuzhou University(2020B005)

Abstract:

The objective of this paper is to discuss the oscillation of a class of second-order dynamic equations with a quasi-linear neutral term on the time measurement chain. Under the regularity condition, by using the generalized Riccati transformation and the classical inequality, and combining with the time scales theory, some new oscillation theorems for the equations are established. The results obtained extend, improve and enrich the part of the study results established in previous literatures. Finally, examples are given to illustrate the applications of the obtained theorems.

Key words: Oscillation, Time scales, Quasilinear neutral, Riccati transformation, Variable delay dynamic equations

CLC Number: 

  • O175.7
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