A biharmonic equation with singular nonlinearity

We study the biharmonic equation ${\mathrm{\Delta }}^{2}u=u^{-\alpha }$, $0<\alpha <1$, in a smooth and bounded domain $\mathrm{\Omega }\subset {\text{RR}}^n$, $n\ge 2$, subject to Dirichlet boundary conditions. Under some suitable assumptions on $\text{o}$ related to the positivity of the Green function for the biharmonic operator, we prove the existence and uniqueness of a solution.