Journal of East China Normal University(Natural Sc ›› 2014, Vol. 2014 ›› Issue (3): 51-59.

• Article • Previous Articles     Next Articles

Oscillation and asymptotic behaviors for third-order delay dynamic equations on time scales

ZHANG Xiao-jian1, YANG Jia-shan2   

  1. 1. Department of Science and Information, Shaoyang University, Shaoyang, Hunan 422004, China;
    2. Department of Mathemedics and Physics, Wuzhou University, Wuzhou  Guangxi 543002, China
  • Received:2013-06-01 Revised:2013-09-01 Online:2014-05-25 Published:2014-07-25

Abstract: The oscillation for certain third-order nonlinear variable
delay dynamic equations on time scales was discussed in this
article. By using the generalized Riccati transformation and a lot
of inequality techniques, we established some new sufficient
conditions which ensure that every solution of the equations either
oscillates or converges to zero. The results extend and improve some
known results. Examples were given to illustrate the main results.

Key words: oscillation, delay dynamic equations, Riccati transformation, inequality techniques, time scales

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