New oscillation criteria for third-order half-linear advanced differential equations

Abstract

The theme of this article is to provide some sufficient conditions for the asymptotic property and oscillation of all solutions of third-order half-linear differential equations with advanced argument of the form $$\left(r_{2}(t)\left(\left(r_{1}(t)\left(y'(t)\right)^α\right)'\right)^β\right)' +q(t)y^γ\left(σ(t)\right)=0,\ t\geq t_{0}>0,$$ where $\int^{\infty}r_{1}^{-\frac{1}α}(s)\text{d}s<\infty$ and $\int^{\infty}r_{2}^{-\frac{1}β}(s)\text{d}s<\infty$. The criteria in this paper improve and complement some existing ones. The results are illustrated by two Euler-type differential equations.