Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 12, pp. 1-12.

Title: Existence of solutions to singular elliptic equations with 
       convection terms via the Galerkin method
       
Authors: Claudianor O. Alves (Univ. Federal de Campina Grande, Brazil)
         Paulo C. Carriao (Univ. Federal de Minas Gerais, Brazil)
         Luiz F. O. Faria (Univ. Federal de Juiz de Fora, Brazil)

Abstract:
 In this article, we use the Galerkin method to show the existence
 of solutions for the following elliptic equation with convection term
 $$
 - \Delta u= h(x,u)+\lambda g(x,\nabla u) \quad
 u(x)>0 \quad  \text{in }  \Omega, \quad
 u=0  \quad \text{on } \partial \Omega,
 $$
 where $\Omega$ is a bounded domain, $\lambda \geq 0$ is a parameter,
 $h$ has sublinear and singular terms, and $g$ is a continuous function.


Submitted June 22, 2009. Published June 18, 2010.
Math Subject Classifications: 35J60, 35B25.
Key Words: Singular elliptic equation; convection term; Galerkin method.