Asymptotic behavior of the unbounded solutions to some degenerate boundary layer equations revisited

We reconsider the boundary-layer flow of a non-Newtonian fluid corresponding to the classical Ostwald de Waele power-law model. The physical problem can be described in terms of solutions of the degenerate differential equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$(|f^{\prime\prime}|^{n-1}f^{\prime\prime})^{\prime} + ff^{\prime\prime} - \beta f^{\prime2} = 0,$$ \end{document}posed on the interval (0, ∞), in which β < 0 and the real number (the power law index) n ≥ 1. This paper deals with the asymptotic behavior of any global unbounded solution; that is a solution satisfying \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\mathop{{\rm lim}}\limits_{\eta\rightarrow\infty}}|f(\eta)| = \infty$$ \end{document}.