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

Abstract

The purpose of this paper is to study the oscillation of second-order half-linear neutral differential equations with advanced argument of the form $\begin{aligned} (r(t)((y(t)+p(t)y(\tau (t)))')^\alpha )'+q(t)y^\alpha (\sigma (t))=0,\ t\geqslant t_0, \end{aligned}$ when $\int _{}^\infty r^{-\frac{1}{\alpha }}(s){\text{d}}s<\infty $. 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.