In this paper, we present further developed results on Hille–Wintner-type integral comparison theorems for second-order half-linear differential equations. Compared equations are seen as perturbations of a given non-oscillatory equation, which allows studying the equations on the borderline of oscillation and non-oscillation. We bring a new comparison theorem and apply it to the so-called generalized Riemann–Weber equation (also referred to as a Euler-type equation).

中文翻译：

---

半线性微分方程的整体比较准则被视为一种扰动

在本文中，我们提出了关于二阶半线性微分方程的Hille-Wintner型积分比较定理的进一步发展结果。比较方程被看作是给定非振荡方程的扰动，这使得可以研究振荡和非振荡边界线上的方程。我们带来了一个新的比较定理，并将其应用于所谓的广义Riemann-Weber方程（也称为Euler型方程）。