Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 93, pp. 1-8.

Title: Asymptotic behaviour of the solution for the singular
       Lane-Emden-Fowler equation with nonlinear convection terms

Author: Zhijun Zhang (Yantai univ., China)
	 
Abstract: 
 We show the exact asymptotic behaviour near the
 boundary for the classical solution to the Dirichler
 problem
 $$
 -\Delta u =k(x)g(u)+\lambda |\nabla u|^q,  \quad u>0,\;
 x\in \Omega,\quad u\big|_{\partial{\Omega}}=0,
 $$
 where $\Omega$ is a bounded domain with smooth boundary in $\mathbb R^N$.
 We use the Karamata regular varying theory, a perturbed argument,
 and constructing comparison functions.
 
Submitted December 23, 2005. Published August 18, 2006.
Math Subject Classifications: 35J65, 35B05, 35O75, 35R05.
Key Words: Semilinear elliptic equations;  Dirichlet problem;  singularity;
    nonlinear convection terms;  Karamata regular variation theory; 
    unique solution; exact asymptotic behaviour.