Electron. J. Diff. Equ., Vol. 2010(2010), No. 12, pp. 1-12.

Existence of solutions to singular elliptic equations with convection terms via the Galerkin method

Claudianor O. Alves, Paulo C. Carriao, Luiz F. O. Faria

Abstract:
In this article, we use the Galerkin method to show the existence of solutions for the following elliptic equation with convection term
$$ - \Delta u= h(x,u)+\lambda g(x,\nabla u) \quad u(x)>0 \quad \hbox{in } \Omega, \quad u=0 \quad \hbox{on } \partial \Omega, $$
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.

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Claudianor O. Alves
Unidade Acadêmica de Matemática e Estatística
Universidade Federal de Campina Grande
58109-970, Campina Grande - PB, Brazil
email: coalves@dme.ufcg.edu.br
Paulo C. Carrião
Departamento de Matemática - Instituto de Ciências Exatas
Universidade Federal de Minas Gerais
30161-970, Belo Horizonte - MG, Brazil
email: carrion@mat.ufmg.br
Luiz F. O. Faria
Departamento de Matemática - Instituto de Ciências Exatas
Universidade Federal de Juiz de Fora
30161-970, Juiz de Fora - MG, Brazil
email: luiz.faria@ufjf.edu.br

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