# Perturbations of the Half-Linear Euler Differential Equation

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## Abstract

Oscillation/nonoscillation properties of the perturbed half-linear Euler differential equation in the critical case are investigated. Strong connections are found between these half-linear differential equations and some linear differential equations, whose coefficient is the perturbation itself. In addition if the solutions of the corresponding linear differential equation satisfy two integral inequalities, then the asymptotic form of the solutions of the half-linear differential equation is established. Examples are given for the latter case.

## Keywords

Differential Equation Riccati Equation Linear Differential Equation Order Differential Equation Integral Inequality
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