Blow-up rates and uniqueness of large solutions for elliptic equations with nonlinear gradient term and singular or degenerate weights |
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Authors: | Yujuan Chen Peter Y H Pang Mingxin Wang |
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Institution: | 1. Department of Mathematics, Nantong University, Nantong, 226007, People’s Republic of China 2. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore, 119076, Republic of Singapore 3. Natural Science Research Center, Harbin Institute of Technology, Harbin, 150080, People’s Republic of China
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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–R?dulescu 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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