Qualitative properties of solutions of some differential equations with an unbounded power potential

For a generalized second-order differential equation of the Emden–Fowler type with an unbounded power potential, we examine the monotonicity and boundary behavior of $\mu$-solutions defined on $(0;+\infty)$ and the asymptotic properties of solutions defined on $(0,h)$, where $h>0$, that tend to $-\infty$ at zero, for various relationships between the parameters $k$, $m$, and $n$.