Solutions of Abel's equation in relation to the asymptotic behaviour of linear differential equations (Q1381546)

Basing on the form of (suitable regular) solutions \(\alpha\) of the Abel equation \[ \alpha \bigl(f(t)\bigr) =\alpha (t)+1 \tag{A} \] the author shows, among others, that solutions to (A) with positive continuous derivatives have comparable rates of increase. The results obtained for (A) are then applied to study the asymptotic behaviour of solutions \(y\) of the ordinary differential equation \[ y''+ p(t) y=0. \tag{Y} \] (For the connections between (A) and (Y) cf. the author [Global properties of ordinary differential equations (1991; Zbl 0784.34009)]).