Morse index and blow-up points of solutions of some nonlinear problems

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作者：
El Mehdi, Khalil [1 ]
Pacella, Filomena [2 ]
机构：
[1] Département de Mathématiques, Faculté des Sciences de Bizerte, Jarzouna 7021 - Bizerte, Tunisia
[2] Dipartimento di Matematica G. Castelnuovo, Università degli Studi di Roma La Sapienza, Piazzale A. Moro, 2, 00185 Roma, Italy
来源：
Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni | 2002年 / 13卷 / 02期
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摘要：
In this Note we consider the following problem & presented equcation; where Ω is a bounded smooth starshaped domain in N, N ≥ 3, pΕ = N+2/N-2 - Ε, Ε > 0, and λ ≥ 0. We prove that if uΕ is a solution of Morse index m > 0 than u cannot have more than m maximum points in Ω for Ε sufficiently small. Moreover if Ω is convex we prove that any solution of index one has only one critical point and the level sets are starshaped for Ε sufficiently small.
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页码：101 / 105
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