Journal of East China Normal University(Natural Sc ›› 2017, Vol. ›› Issue (3): 54-63.doi: 10.3969/j.issn.1000-5641.2017.03.006

• Mathematics • Previous Articles     Next Articles

New results of oscillation for certain second-order nonlinear dynamic equations on time scales

YANG Jia-shan1,2, ZHANG Xiao-jian3   

  1. 1. School of Information and Electronic Engineering, Wuzhou University, Wuzhou Guangxi 543002, China;
    2. Laboratory of Complex System Simulation and Intelligent Computing, Wuzhou University, Wuzhou Guangxi 543002, China;
    3. Department of Science and Information, Shaoyang University, Shaoyang Hunan 422004, China
  • Received:2016-08-28 Online:2017-05-25 Published:2017-05-18


This paper is concerned with oscillatory behavior of the following second-order nonlinear neutral variable delay functional dynamic equations


on a time scale T, where Φu)=|u|λ-1u (hereλ> 0 is an arbitrary constant). By using a couple of Riccati substitutions, the time scales theory and inequality technique, we establish two new oscillation criteria for the equations, these results deal with some cases not covered by existing results in the literature. Finally, two examples are presented to illustrate the importance of our theorems.

Key words: oscillation, time scales, functional dynamic equations, variable delay

CLC Number: