Abstract
We study the Dirichlet problem for the Hénon equation
where Ω is the unit ball in \(\mathbb{R}^N\), with N ≥ 3, the power α is positive and \(\varepsilon\) 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 \(\varepsilon\) goes to zero. We also show that the ground state solution (which blows up at one point) is unique.
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The first author is supported by the M.I.U.R. National Project “Metodi variazionali e topologici nello studio di fenomeni non lineari” . The second author is supported by the M.I.U.R. National Project “Metodi variazionali ed equazioni differenziali nonlineari”.
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Pistoia, A., Serra, E. Multi-peak solutions for the Hénon equation with slightly subcritical growth. Math. Z. 256, 75–97 (2007). https://doi.org/10.1007/s00209-006-0060-9
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DOI: https://doi.org/10.1007/s00209-006-0060-9