In this paper we discuss the ordering properties of positive radial solutions of the equation Δpu(x)+k|x|δuq-1(x)=0\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} \\Delta _p u(x)+ k |x|^{\\delta } u^{q-1}(x)=0 \\end{aligned}$$\\end{document}where x in {mathbb {R}}^n, n>p>1, k>0, delta>-p, q>p. We are interested both in regular ground states u (GS), defined and positive in the whole of {mathbb {R}}^n, and in singular ground states v (SGS), defined and positive in {mathbb {R}}^n setminus {0} and such that lim _{|x| rightarrow 0} v(x)=+infty . A key role in this analysis is played by two bifurcation parameters p^{JL}(delta ) and p_{jl}(delta ), such that p^{JL}(delta )>p^*(delta )>p_{jl}(delta )>p: p^{JL}(delta ) generalizes the classical Joseph–Lundgren exponent, and p_{jl}(delta ) its dual. We show that GS are well ordered, i.e. they cannot cross each other if and only if q ge p^{JL}(delta ); this way we extend to the p>1 case the result proved in Miyamoto (Nonlinear Differ Equ Appl 23(2):24, 2016), Miyamoto and Takahashi (Arch Math Basel 108(1):71–83, 2017) for the p ge 2 case. Analogously we show that SGS are well ordered, if and only if q le p_{jl}(delta ); this latter result seems to be known just in the classical p=2 and delta =0 case, and also the expression of p_{jl}(delta ) has not appeared in literature previously.