A biharmonic equation with singular nonlinearity

Abstract

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

Cited by in corpus (1)

• Some remarks on biharmonic elliptic problems with a singular nonlinearity