Rectifiable and unrectifiable oscillations for a class of second-order linear differential equations of Euler type

The main purpose of the paper is to pay attention to a new kind of oscillations, so-called rectifiable and unrectifiable oscillations, which occur in a class of linear second-order differential equations, including the famous linear Euler differential equation. It will be shown that this kind of oscillations only depends on a positive real parameter which appears in a singular term of the main equation as well as in a suitable boundary-layer condition.