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

Saïma Khenissy, Olivier Rey

• 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.