Some Novel Conditions for the Oscillation of Second-Order Noncanonical Dynamic Equations with Non-linear Neutral Terms

The aim of this paper is to study the oscillatory behavior of solutions of second-order noncanonical dynamical equations with a sublinear and superlinear neutral terms. Using the process of linearization, we obtain some new easily verifiable criteria for the oscillation of the aforementioned equation. The results are illustrated by three examples. The results are new even for the case T=R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {T}}={\mathbb {R}}$$\end{document} and T=Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {T}}={\mathbb {Z}}$$\end{document}.