Blow-up rates and uniqueness of large solutions for elliptic equations with nonlinear gradient term and singular or degenerate weights

This paper deals with the blow-up rate and uniqueness of large solutions of the elliptic equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta u = b(x)f(u)+c(x)g(u)|\nabla u|^q}$$\end{document} in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Omega \subset \mathbb{R}^N}$$\end{document}, where q > 0, f(u) and g(u) are regularly varying functions at infinity, and the weight functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${b(x),\,c(x) \in C^\alpha(\Omega,\,\mathbb{R}^+)}$$\end{document}, 0 < α < 1, may be singular or degenerate on the boundary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\partial\Omega}$$\end{document}. Combining the regular variation theoretic approach of Cîrstea–Rădulescu and the systematic approach of Bandle–Giarrusso, we are able to improve and generalize most of the previously available results in the literature.