Oscillation of Emden–Fowler type nonlinear neutral delay dynamic equation on time scales

Abstract

In this paper, we consider the following Emden–Fowler type nonlinear neutral delay dynamic equation of the form $$\begin{aligned} \left( r(t)\left( (y(t)+p(t)y(\tau (t)))^\Delta \right) ^\alpha \right) ^\Delta +q(t)y^\beta (m(t))=0 \end{aligned}$$ on time scales, where $$\alpha $$ and $$\beta $$ are ratios of two odd positive integers. Specially, $$\alpha $$ , $$\beta $$ are arbitrary and without any conditional restrictions, which are completely new compared with previous references. Some new oscillatory and asymptotic properties are obtained by means of inequality technique and Riccati transformation. The results obtained generalize and improve some of the results of Agarwal and Džurina et al.