Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 04, pp. 1-11.

Title: Positive solutions for elliptic equations with singular nonlinearity

Authors: Junping Shi (College of William and Mary, Williamsburg, VA, USA)
         Miaoxin Yao (Tianjin Univ. China)

Abstract: 
 We study an elliptic boundary-value problem with singular
 nonlinearity via the method of monotone iteration scheme:
 $$\displaylines{
 -\Delta u(x)=f(x,u(x)),\quad x \in \Omega,\cr
 u(x)=\phi(x),\quad x \in \partial \Omega ,
 }$$
 where $\Delta$ is the Laplacian operator, $\Omega$ is a bounded domain
 in $\mathbb{R}^{N}$, $N \geq 2$, $\phi \geq 0$ may take the value $0$
 on $\partial\Omega$, and $f(x,s)$ is possibly singular near $s=0$.
 We prove the existence and the uniqueness of positive solutions
 under a set of hypotheses that do not make neither monotonicity nor
 strict positivity assumption on $f(x,s)$, which improvements of
 some previous results.

Submitted August 15, 2004. Published January 2, 2005.
Math Subject Classifications: 35J25, 35J60.
Key Words: Singular nonlineararity; elliptic equation; positive solution;
           monotonic iteration.