Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2022, Vol. 39 ›› Issue (2): 292-308.doi: 10.3969/j.issn.1005-3085.2022.02.009

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Oscillation of Third-order Nonlinear Emden-Fowler Delay Dynamic Equation with a Sublinear Neutral Term on Time Scales

ZHANG Zhiyu1,   FENG Ruihua2   

  1. 1. Department of Science, Taiyuan Institute of Technology, Taiyuan 030008
    2. School of Science, North University of China, Taiyuan 030051
  • Online:2022-04-15 Published:2022-06-15
  • Supported by:
    The National Natural Science Foundation of China (11701528; 11647034); the Natural Science Foundation of Shanxi Province (2011011002-3).

Abstract:

Judging the oscillation and asymptotic behavior of delay dynamic equations on time scale plays an important role in mathematical physics, automatic control theory and engineering, infectious disease model analysis, bridge design and so on. Thus, the oscillation behavior of third-order nonlinear Emden-Fowler type delay dynamic equation with a sublinear neutral term on time scales are investigated. By using the dynamic calculus on time scales, generalized Riccati transformation and inequality technique, two oscillation theorems to ensure that every solution of the equation oscillates or converges to zero are obtained. These results extend and improve the results established in previous literatures. Finally, the effectiveness of the theoretical results obtained here are illustrated with two examples.

Key words: time scale, sublinear neutral term, time delay, dynamic equation, oscillation

CLC Number: