Oscillation criteria for a class of second-order Emden-Fowler delay dynamic equations on time scales

作者：Han Zhenlai^*; Sun Shurong; Shi Bao

来源：Journal of Mathematical Analysis and Applications, 2007, 334(2): 847-858.

DOI：10.1016/j.jmaa.2007.01.004

• oscillation
• second-order
• delay dynamic equations
• time scale

By means of Riccati transformation technique, we establish some new oscillation criteria for the secon-dorder Emden-Fowler delay dynamic equations
x(Delta Delta)(t) + p(t)x(gamma) (tau(t)) = 0
on a time scale T; here gamma is a quotient of odd positive integers with p(t) real-valued positive rd-continuous functions defined on T. To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales. Our results in this paper not only extend the results given in [R.P. Agarwal, M. Bohner, S.H. Saker, Oscillation of second-order delay dynamic equations, Can. Appl. Math. Q 13 (1) (2005) 1-18] but also unify the oscillation of the second-order Emden-Fowler delay differential equation and the second-order Emden-Fowler delay difference equation.

• 出版日期2007-10-15
• 单位中国人民解放军海军航空工程学院; 暨南大学