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 ›› 2023, Vol. 40 ›› Issue (2): 265-280.doi: 10.3969/j.issn.1005-3085.2023.02.007

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Dynamical Properties of Certain Second-order Delay Nonlinear Noncanonical Dynamic Equations on Time Scales

ZHANG Ping1,   YANG Jiashan2   

  1. 1. School of Science, Shaoyang University, Shaoyang, Hunan 422004
    2. School of Data Science and Software Engineering, Wuzhou University, Wuzhou, Guangxi 543002
  • Received:2020-12-06 Accepted:2021-06-08 Online:2023-04-15 Published:2023-06-20
  • Contact: J. Yang. E-mail address: syxyyjs@163.com
  • Supported by:
    The National Natural Science Foundation of China (51765060); the Scientific Research Fund of Education Department of Hunan Province (20C1683).

Abstract:

The analysis theory on the time scales not only effectively unifies the theory of continuous analysis and discrete analysis, but also becomes an indispensable mathematics tool in such domains of natural science and social science. Moreover, the oscillation and non-oscillation theories are the key issues of qualitative study of the neutral dynamic equations, which have attracted people's attention. Therefore, the dynamical properties of certain second-order delay nonlinear noncanonical dynamic equations on time scales are discussed. By using the calculus theory on the time scales and the generalized Riccati transformation and some necessary analytic techniques, two new dynamical properties for the equations under certain conditions are established. The results extend and improve the part of the results established in previous literatures. Finally, the effectiveness of the theoretical results are verified by two examples.

Key words: oscillation, time scales, Emden-Fowler dynamic equations, damping term, nonlinear

CLC Number: