Existence of solutions to singular elliptic equations with convection terms via the Galerkin method
Claudianor O. Alves, Paulo César Carrião, Luiz F. O. Faria · DOAJ (DOAJ: Directory of Open Access Journals) · 2010
In this article, we use the Galerkin method to show the existence of solutions for the following elliptic equation with convection term $$ - Delta u= h(x,u)+lambda g(x, abla u) quad u(x)>0 quad ext{in } Omega, quad u=0 quad ext{on } partial Omega, $$ where $Omega$ is a bounded domain, $lambda geq 0$ is a parameter, $h$ has sublinear and singular terms, and $g$ is a continuous function.