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A biharmonic equation with singular nonlinearity

Part of: Nonlinear integral equations Nonlinear operators and their properties Elliptic equations and systems

Published online by Cambridge University Press:  14 June 2011

Marius Ghergu
Marius Ghergu
Affiliation:
School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland ([email protected])
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Abstract

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We study the biharmonic equation Δ2u = u−α, 0 < α < 1, in a smooth and bounded domain Ω ⊂ ℝn, n ≥ 2, subject to Dirichlet boundary conditions. Under some suitable assumptions on Ω related to the positivity of the Green function for the biharmonic operator, we prove the existence and uniqueness of a solution.

Keywords

biharmonic operatorsingular nonlinearityGreen functionintegral equation

MSC classification

Secondary: 35J40: Boundary value problems for higher-order elliptic equations 35J08: Green's functions 45G05: Singular nonlinear integral equations 47H10: Fixed-point theorems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 1 , February 2012 , pp. 155 - 166
Copyright
Copyright © Edinburgh Mathematical Society 2011

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