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.