We deal with Euler‐type half‐linear second‐order differential equations, and our intention is to derive conditions in order their non‐trivial solutions are non‐oscillatory. This paper connects to the article P. Hasil, J. Šišoláková, M. Veselý: Averaging technique and oscillation criterion for linear and half‐linear equations, Appl. Math. Lett. 92 (2019), 62–69, where the corresponding oscillatory counterpart is studied and an oscillation criterion is established. The used effective technique for this investigation is the combination of the generalized adapted Prüfer angle and the modified Riccati transformation. This paper is completed by two corollaries and an example concerning the linear case when we obtain new results as well.

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具有无穷系数的线性和半线性微分方程的非振动性

我们处理Euler型半线性二阶微分方程，我们的目的是推导条件，以便它们的非平凡解是非振动性的。本文与文章P. Hasil，J.Šišoláková，M.Veselý相关：线性和半线性方程的平均技术和振动准则，Appl。数学。来吧 92（2019），62-69，其中研究了相应的振荡对应物并建立了振荡准则。这项研究使用的有效技术是广义适应的Prüfer角度和修正的Riccati变换的结合。本文由两个推论和一个关于线性情况的例子完成，当我们也获得新结果时。