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arXiv · 0911.0308

A biharmonic equation with singular nonlinearity

Marius Ghergu
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Abstract

We study the biharmonic equation $Δ^2 u =u^{-α}$, $0<α<1$, in a smooth and bounded domain $Ω\subset\RR^n$, $n\geq 2$, 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.

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Marius Ghergu. 2009-11-02. A biharmonic equation with singular nonlinearity. https://arxiv.org/abs/0911.0308

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