In this paper we look for positive solutions of the problem −Deltau + λu = up−1 in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in Rn, n greater than 2,p >2 and λ is a positive parameter.We describe new concentration phenomena, which occur as λ→+∞, and exploit them to construct (for λ large enough) positive solutions that concentrate near spheres of codimension 2 as λ→+∞; these spheres approach the boundary of Ω as λ→+∞. Notice that the existence and multiplicity results we obtain hold also in contractible domains arbitrarily close to starshaped domains (no solution can exist if p greater than or equal to 2n/(n−2) and Ω is starshaped, because of Pohožaev’s identity).
Concentration phenomena for solutions of superlinear elliptic problems
PASSASEO, Donato
2006-01-01
Abstract
In this paper we look for positive solutions of the problem −Deltau + λu = up−1 in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in Rn, n greater than 2,p >2 and λ is a positive parameter.We describe new concentration phenomena, which occur as λ→+∞, and exploit them to construct (for λ large enough) positive solutions that concentrate near spheres of codimension 2 as λ→+∞; these spheres approach the boundary of Ω as λ→+∞. Notice that the existence and multiplicity results we obtain hold also in contractible domains arbitrarily close to starshaped domains (no solution can exist if p greater than or equal to 2n/(n−2) and Ω is starshaped, because of Pohožaev’s identity).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
