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.