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

                     $(r_2(t)((r_1(t)(y′(t))^α)′)^β)′ + q(t)y^γ(σ(t)) = 0$,    $t ≥ t_0 > 0,$

where $∫^∞ r_1^{-\frac{1}{α}}(s)ds < ∞$ and $∫^∞r_2^{-\frac{1}{β}}(s)ds < ∞$. The criteria in this paper improve and complement some existing ones. The results are illustrated by two Euler-type differential equations.