论文标题
三阶半线性高级微分方程的新振荡标准
New oscillation criteria for third-order half-linear advanced differential equations
论文作者
论文摘要
本文的主题是提供一些足够条件，以使所有三阶半线性微分方程的渐近属性和振荡具有高级$ $ \ left（r_ {2}（t）（t）\ left（\ left（r_ {1}（r_ {1}（t）（t）（t）\左（y'（y'（y'（y'）， +q（t）y^γ\ left（σ（t）\ right）= 0，\ t \ geq t_ {0}> 0，$$其中$ \ int^{\ infty} r_ {1}^{ - \ frac {1} $ \ int^{\ infty} r_ {2}^{ - \ frac {1}β}（s）\ text {d} s <\ infty $。本文中的标准改善并补充了一些现有标准。结果由两个Euler型微分方程说明。
The theme of this article is to provide some sufficient conditions for the asymptotic property and oscillation of all solutions of third-order half-linear differential equations with advanced argument of the form $$\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.
