Electron. J. Diff. Equ., Vol. 2014 (2014), No. 183, pp. 1-12.

Exact boundary behavior of solutions to singular nonlinear Dirichlet problems

Bo Li, Zhijun Zhang

In this article we analyze the exact boundary behavior of solutions to the singular nonlinear Dirichlet problem
-\Delta u=b(x)g(u)+\lambda a(x) f(u), \quad u>0, \quad x \in
 \Omega,\quad u|_{\partial \Omega}=0,
where $\Omega$ is a bounded domain with smooth boundary in $\mathbb{R}^N$, $\lambda> 0$, $g\in C^1((0,\infty), (0,\infty))$, $\lim_{s \to 0^+}g(s)=\infty$, $b, a \in C_{\rm loc}^{\alpha}({\Omega})$, are positive, but may vanish or be singular on the boundary, and $f\in C([0, \infty), [0, \infty))$.

Submitted July 11, 2014. Published August 29, 2014.
Math Subject Classifications: 35J65, 35B05, 35J25, 60J50.
Key Words: Semilinear elliptic equation; singular Dirichlet problem; positive solution; boundary behavior.

Show me the PDF file (261 KB), TEX file, and other files for this article.

Bo Li
School of Mathematics and Statistics, Lanzhou University
Lanzhou 730000, Gansu, China
email: libo_yt@163.com
Zhijun Zhang
School of Mathematics and Information Science
Yantai University, Yantai 264005, Shandong, China
email: chinazjzhang2002@163.com, zhangzj@ytu.edu.cn

Return to the EJDE web page