三阶半线性超前微分方程的新振动准则
New oscillation criteria for third-order half-linear advanced differential equations
摘要：
给出了一类具有超前变元的三阶半线性微分方程解的渐近性和振动性的充分条件，其中$\int^{\infty}r_{1}^{-\frac{1}α}(s)\text{d}s<\infty$和$\int^{\infty}r_{2}^{-\frac{1}β}(s)\text{d}s<\infty$为$$\left(r_{2}(t)\left(\left(r_{1}(t)\left(y'(t)\right)^α\right)'\right)^β\right)' +q(t)y^γ\left(σ(t)\right)=0,\ t\geq t_{0}>0,$$.本文的准则改进和补充了一些现有的准则。结果用两个欧拉型微分方程来说明。
英文摘要：
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.
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