On a Biharmonic Equation Involving Nearly Critical Exponent

Details On a Biharmonic Equation Involving Nearly Critical Exponent On a Biharmonic Equation Involving Nearly Critical Exponent

2004-01-07

arxiv.org/abs/math/0401061v1

Mathematics

Analysis of PDEs

23 pages

Scientific paper

This paper is concerned with a biharmonic equation under the Navier boundary condition with nearly critical exponent. We study the asymptotic behavior os solutions which are minimizing for the Sobolev quatient. We show that such solutions concentrate around an interior point which is a critical point of the Robin's function. Conversely, we show that for any nondegenerate critical point fo the Robin's function, the exist solutions concentrating around such a point. Finally, we prove that, in contrast with what happened in the subcritical equation, the supercritical problem has no solutions which concentrate around a point .

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