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).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/103894
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