The paper deals with the existence of positive solutions of the problem −Delta u = u^ p in \Omega, u = 0 on ∂\Omega, where \Omega is a bounded domain of Rn, n ≥ 3, and p > 2. We describe new concentration phenomena, which arise as p →+∞ and can be exploited in order to construct, for p large enough, positive solutions that concentrate, as p → +∞, near submanifolds of codimension 2.
Nonlinear elliptic equations with large supercritical exponents
PASSASEO, Donato
2006-01-01
Abstract
The paper deals with the existence of positive solutions of the problem −Delta u = u^ p in \Omega, u = 0 on ∂\Omega, where \Omega is a bounded domain of Rn, n ≥ 3, and p > 2. We describe new concentration phenomena, which arise as p →+∞ and can be exploited in order to construct, for p large enough, positive solutions that concentrate, as p → +∞, near submanifolds of codimension 2.File in questo prodotto:
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