Oscillation of Second-Order Half-Linear Neutral Advanced Differential Equations

The purpose of this paper is to study the oscillation of second-order half-linear neutral differential equations with advanced argument of the form (r(t)((y(t)+p(t)y(τ(t)))′)α)′+q(t)yα(σ(t))=0,t⩾t0,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} (r(t)((y(t)+p(t)y(\tau (t)))')^\alpha )'+q(t)y^\alpha (\sigma (t))=0,\ t\geqslant t_0, \end{aligned}$$\end{document}when ∫∞r-1α(s)ds<∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\int _{}^\infty r^{-\frac{1}{\alpha }}(s){\text{d}}s<\infty $$\end{document}. We obtain sufficient conditions for the oscillation of the studied equations by the inequality principle and the Riccati transformation. An example is provided to illustrate the results.