On a Biharmonic Equation Involving Nearly Critical Exponent

2004/01/07 by Mohamed Ben Ayed, Ayed, Mohamed Ben, Khalil El Mehdi +1
Mathematics · #35J40 #35J65 #58E05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35J40 #msc:35J65 #msc:58E05

paper · pdf · doi:10.48550/arxiv.math/0401061

23 pages

arxiv created 2004/01/07 · arxiv updated 2009/12/01

Abstract

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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