Oscillation Criteria for Certain Fourth-Order Nonlinear Delay Differential Equations

In this article, we establish some new criteria for the oscillation of fourth-order nonlinear delay differential equations of the form (r2(t)(r1(t)(y′′(t))α)′)′+p(t)(y′′(t))α+q(t)f(y(g(t)))=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(r_2(t)(r_1(t)(y''(t))^\alpha)')' + p(t)(y''(t))^\alpha + q(t)f(y(g(t))) = 0$$\end{document}provided that the second-order equation (r2(t)z′(t))′)+p(t)r1(t)z(t)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(r_2(t)z'(t))') + \frac{p(t)}{r_1(t)}z(t) = 0$$\end{document}is nonoscillatory or oscillatory.