We study the Dirichlet problem for the Hénon equation where Ω is the unit ball in , with N ≥ 3, the power α is positive and is a small positive parameter. We prove that for every integer k ≥ 1 the above problem has a solution which blows up at k different points of ∂Ω as goes to zero. We also show that the ground state solution (which blows up at one point) is unique
Multi-peak solutions for the Henon equation with slightly subcritical growth / Angela Pistoia, Enrico Serra. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 256:1(2007), pp. 75-97.
Multi-peak solutions for the Henon equation with slightly subcritical growth
Enrico Serra
2007
Abstract
We study the Dirichlet problem for the Hénon equation where Ω is the unit ball in , with N ≥ 3, the power α is positive and is a small positive parameter. We prove that for every integer k ≥ 1 the above problem has a solution which blows up at k different points of ∂Ω as goes to zero. We also show that the ground state solution (which blows up at one point) is unique
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