Quasilinear elliptic equation involving singular non-linearities.

We consider the existence of solutions for the quasilinear elliptic equation [image omitted] under Dirichlet boundary conditions, where Ω⊂RN is a bounded domain with smooth boundary. The most important fact here is that either g or f (or both of them) is singular at 0 if g(t), [image omitted] . By means of a direct variational approach, we establish the existence of a solution with [image omitted] -norms. [ABSTRACT FROM AUTHOR]