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Boundary blow-up solutions for elliptic equations with gradient terms and singular weights: existence, asymptotic behaviour and uniqueness

Published online by Cambridge University Press:  15 July 2011

Yujuan Chen  and
Mingxin Wang
Yujuan Chen
Affiliation:
Department of Mathematics, Nantong University, Nantong 226007, People's Republic of China
Mingxin Wang
Affiliation:
Natural Science Research Center, Harbin Institute of Technology, Harbin 150080, People's Republic of China (mxwang@seu.edu.cn)
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Abstract

This paper deals with the non-negative boundary blow-up solutions of the equation ∆u = b(x)up + c(x)uσ|∇u|q in Ω ⊂ ℝ,N, where b(x), c(x) ∈ Cγ (Ω,ℝ+) for some 0 < γ < 1 and can be vanishing or singular on the boundary, and p, σ and q are non-negative constants. The existence and asymptotic behaviour of such a solution near the boundary are investigated, and we show how the nonlinear gradient term affects the results. As a consequence of the asymptotic behaviour, we also show the uniqueness result.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 4 , August 2011 , pp. 717 - 737
Copyright
Copyright © Royal Society of Edinburgh 2011

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