We compute the Morse index of 1-spike solutions of the semilinear elliptic problem () where is a smooth bounded domain and is sufficiently large. When Ω is convex, our result, combined with the characterization in [21], a result in [40] and with recent uniform estimates in [37], gives the uniqueness of the solution to (), for p large. This proves, in dimension two and for p large, a longstanding conjecture.
Morse index and uniqueness of positive solutions of the Lane-Emden problem in planar domains / De Marchis, F.; Grossi, M.; Ianni, I.; Pacella, F.. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - (2019). [10.1016/j.matpur.2019.02.011]
Morse index and uniqueness of positive solutions of the Lane-Emden problem in planar domains
De Marchis, F.;Grossi, M.;Ianni, I.;Pacella, F.
2019
Abstract
We compute the Morse index of 1-spike solutions of the semilinear elliptic problem () where is a smooth bounded domain and is sufficiently large. When Ω is convex, our result, combined with the characterization in [21], a result in [40] and with recent uniform estimates in [37], gives the uniqueness of the solution to (), for p large. This proves, in dimension two and for p large, a longstanding conjecture.| File | Dimensione | Formato | |
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