This paper deals with the asymptotic behavior of solutions of the half-linear differential equation

$$\begin{aligned} (p(t)|x'|^{\alpha }\mathrm {sgn}\,x')' + q(t)|x|^{\alpha }\mathrm {sgn}\,x = 0, \quad t \ge t_{0}. \end{aligned}$$

It will be shown that, for any solution x(t) of this equation, there are only two types of asymptotic behavior as \(t\rightarrow \infty \).

中文翻译：

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半线性常微分方程非振动解的渐近行为

本文研究半线性微分方程解的渐近性质

$$ \ begin {aligned}（p（t）| x'| ^ {\ alpha} \ mathrm {sgn} \，x'）'+ q（t）| x | ^ {\ alpha} \ mathrm {sgn} \，x = 0，\ quad t \ ge t_ {0}。\ end {aligned} $$

将表明，对于该方程的任何解x（t），只有两种渐近行为，如\（t \ rightarrow \ infty \）。