Existence of solutions to singular elliptic equations with convection terms via the Galerkin method - Claudianor Oliveira Alves; Paulo C. Carriao; Luiz F. O. Faria (Electronic Journal of Differential Equations, 2010)
In this article, we use the Galerkin method to show the existence of solutions for the following elliptic equation with convection term $$ - Delta u= h(x,u)+lambda g(x, abla u) quad u(x)>0 quad extin Omega, quad u=0 quad exton partial Omega, $$ where $Omega$ is a bounded domain, $lambda geq 0$ is a parameter, $h$ has sublinear and singular terms, and $g$ is a continuous function.