A biharmonic equation with singular nonlinearity

Details A biharmonic equation with singular nonlinearity A biharmonic equation with singular nonlinearity

2009-11-02

arxiv.org/abs/0911.0308v1

Mathematics

Analysis of PDEs

Scientific paper

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

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