A boundary blow-up for sub-linear elliptic problems with a nonlinear gradient term
Files
Date
2006-05-20
Authors
Zhang, Zhijun
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
By a perturbation method and constructing comparison functions, we show the exact asymptotic behaviour of solutions to the semilinear elliptic problem
Δu - |∇u|q = b(x)g(u), u > 0 in Ω, u|∂Ω = +∞,
where Ω is a bounded domain in ℝN with smooth boundary, q ∈ (1, 2], g ∈ C[0, ∞) ∩ C1 (0, ∞), g(0) = 0, g is increasing on [0, ∞), and b is non-negative non-trivial in Ω, which may be singular or vanishing on the boundary.
Description
Keywords
Semilinear elliptic equations, Large solutions, Asymptotic behaviour
Citation
Zhang, Z. (2006). A boundary blow-up for sub-linear elliptic problems with a nonlinear gradient term. <i>Electronic Journal of Differential Equations, 2006</i>(64), pp. 1-9.