Abstract
This paper deals with the blow-up rate and uniqueness of large solutions of the elliptic equation \({\Delta u = b(x)f(u)+c(x)g(u)|\nabla u|^q}\) in \({\Omega \subset \mathbb{R}^N}\), where q > 0, f(u) and g(u) are regularly varying functions at infinity, and the weight functions \({b(x),\,c(x) \in C^\alpha(\Omega,\,\mathbb{R}^+)}\), 0 < α < 1, may be singular or degenerate on the boundary \({\partial\Omega}\). 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.
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Chen, Y., Pang, P.Y.H. & Wang, M. Blow-up rates and uniqueness of large solutions for elliptic equations with nonlinear gradient term and singular or degenerate weights. manuscripta math. 141, 171–193 (2013). https://doi.org/10.1007/s00229-012-0567-9
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DOI: https://doi.org/10.1007/s00229-012-0567-9