We compute the Morse index (up) of any radial solution up of the semilinear problem: −Δu=|x|^α|u|^(p−1)u in B u=0 on ∂B where B is the unit ball of ℝ^2 centered at the origin, α≥0 is fixed and p>1 is sufficiently large. In the case α=0, i.e. for the Lane-Emden problem, this leads to the following Morse index formula (up)=4m2−m−2, for p large enough, where m is the number of nodal domains of u.
Morse index computation for radial solutions of the Henon problem in the disk / LISA AMADORI, Anna; DE MARCHIS, Francesca; Ianni, Isabella. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 215(2022). [10.1016/j.na.2021.112645]
Morse index computation for radial solutions of the Henon problem in the disk
FRANCESCA DE MARCHIS;ISABELLA IANNI
2022
Abstract
We compute the Morse index (up) of any radial solution up of the semilinear problem: −Δu=|x|^α|u|^(p−1)u in B u=0 on ∂B where B is the unit ball of ℝ^2 centered at the origin, α≥0 is fixed and p>1 is sufficiently large. In the case α=0, i.e. for the Lane-Emden problem, this leads to the following Morse index formula (up)=4m2−m−2, for p large enough, where m is the number of nodal domains of u.File allegati a questo prodotto
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