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

Abstract By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order Emden–Fowler delay dynamic equations x Δ Δ ( t ) + p ( t ) x γ ( τ ( t ) ) = 0 on a time scale T ; here γ 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.

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