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

Abstract

This paper deals with the blow-up rate and uniqueness of large solutions of the elliptic equation Δu = b(x)f(u) + c(x)g(u){pipe}∇u{pipe}q, where q > 0, f(u) and g(u) are regularly varying functions at infinity, and the weight functions b(x), c(x) ∈ Cα(Ω, ℝ+) 0 < α < 1, may be singular or degenerate on the boundary ∂Ω. Combining the regular variation theoretic approach of Cîrstea-Rǎdulescu and the systematic approach of Bandle-Giarrusso, we are able to improve and generalize most of the previously available results in the literature. © 2012 Springer-Verlag.