Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
 
Abstract : For $q$ close to ${N+2\over N-2}$, $N\geq 3$, positive solutions of $\Delta u + \lambda u + u^q = 0$ in a bounded, smooth domain $\Omega$ in $\R^N$, with zero Dirichlet boundary conditions, are considered. For $N=3$, existence in the super- and sub-critical regimes is stated and a duality between both cases is established. Under additional symmetry conditions, multiplicity corresponding to towers of bubbles holds in the super-critical regime. A sketch of the proofs is provided. The case $N\geq 4$ is also treated.
 
 
DUALITY IN SUB-SUPERCRITICAL BUBBLING IN THE BREZIS-NIRENBERG PROBLEM NEAR THE CRITICAL EXPONENT
DEL PINO Manuel, DOLBEAULT Jean, MUSSO Monica
2004-9
23-01-2004
 
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