We study the Dirichlet problem for the Hénon equation −Δu=|x|αuN+2N−2−εu>0u=0in Ω,in Ω,on ∂Ω, where Ω is the unit ball in RN, with N≥3, the power α is positive and ε 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 ε goes to zero. We also show that the ground state solution (which blows up at one point) is unique.
Multi--peak solutions for the H'enon equation with slightly subcritical growth / Pistoia, Angela; E., Serra. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - 256:(2007), pp. 75-97. [10.1007/s00209-006-0060-9]
Multi--peak solutions for the H'enon equation with slightly subcritical growth
PISTOIA, Angela;
2007
Abstract
We study the Dirichlet problem for the Hénon equation −Δu=|x|αuN+2N−2−εu>0u=0in Ω,in Ω,on ∂Ω, where Ω is the unit ball in RN, with N≥3, the power α is positive and ε 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 ε goes to zero. We also show that the ground state solution (which blows up at one point) is unique.File allegati a questo prodotto
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