Electron. J. Diff. Eqns., Vol. 2006(2006), No. 93, pp. 1-8.

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

Zhijun Zhang

Abstract:
We show the exact asymptotic behaviour near the boundary for the classical solution to the Dirichler problem
$$ -\Delta =k(x)g(u)+\lambda |\nabla u|^q, \quad u greater than 0,\; x\in \Omega,\quad u\big|_{\partial{\Omega}}=0, $$
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.

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Zhijun Zhang
Department of Mathematics and Informational Science
Yantai University, Yantai, Shandong, 264005, China
email: zhangzj@ytu.edu.cn

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