Asymptotics of solutions of Emden-Fowler-type equations (Q2353053)

Consider the scalar differential equation \[ y^{(n)}(x)= p(x)|y(k)|^\sigma \text{sgn\,}y(x)\tag{\(*\)} \] under the assumption that \(p\) has the power asymptotics \[ p(x)= ax^\beta(1+ \sigma(x^{-\varepsilon}))\quad\text{as }x\to+\infty, \] where \(a\neq 0\), \(\varepsilon>0\). The author determines the power asymptotics of right continuable solutions of \((*)\) and presents solutions with power-logarithmic asymptotics.