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

By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order Emden–Fowler delay dynamic equationsxΔΔ(t)+p(t)xγ(τ(t))=0xΔΔ(t)+p(t)xγ(τ(t))=0 on a time scale TT; here γ   is a quotient of odd positive integers with p(t)p(t) real-valued positive rd-continuous functions defined on TT. 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.