Nonlinear Second Order Delay Dynamic Equations on Time Scales: New Oscillatory Criteria

In the paper, we present some new oscillation results for the second order nonlinear delay dynamic equation of the form r(θ)(zΔ(θ))αΔ+q(θ)zν(ω(θ))=0forθ∈T0=[θ0,∞)∩T.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \left( r(\theta )(z^{\Delta }(\theta ))^{\alpha }\right) ^{\Delta } +q(\theta )z^{\nu }(\omega (\theta ))=0\;\text {for}\;\theta \in {\mathbb {T}}_{0}=[\theta _{0},\infty )\cap {\mathbb {T}}. \end{aligned}$$\end{document}We derive new monotonic properties of the nonoscillatory solutions and utilizing them to linearize the considered equation. The presented results are verified by some illustrative examples.