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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.
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.