A Criterion for Existence of Solutions to the Supercritical Bahri-Coron's Problem

• Autores: Saïma Khenissy, Olivier Rey
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 30, Nº 2, 2004, págs. 587-613
• Idioma: inglés
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• Resumen

  • We consider a second order Dirichlet elliptic problem with slightly supercritical nonlinearity, on a smooth and bounded three dimensional domain W. We prove that nontriviality of the relative homology between the level sets of some function j in W¥ W, involving the Green's function and its regular part, implies the existence of a solution to the problem which blows up, as the nonlinearity goes to critical growth, at two points, which correspond to a critical point of j.