We are concerned with the Lane-Emden problem −∆u = u^P in Ω u > 0 in Ω u = 0 on ∂Ω, where Ω ⊂ R^2 is a smooth bounded domain and p > 1 is sufficiently large. Improving some known asymptotic estimates on the solutions, we prove the non-degeneracy and local uniqueness of the multi-spikes positive solutions for general domains. Our methods mainly use ODE’s theory, various local Pohozaev identities, blow-up analysis and the properties of Green’s function.

Non-degeneracy and local uniqueness of positive solutions to the Lane-Emden problem in dimension two / Grossi, Massimo; Ianni, Isabella; Luo, Peng; Yan, Shusen. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 1776-3371. - 157(2022), pp. 145-210.

Non-degeneracy and local uniqueness of positive solutions to the Lane-Emden problem in dimension two

MASSIMO GROSSI;ISABELLA IANNI;
2022

Abstract

We are concerned with the Lane-Emden problem −∆u = u^P in Ω u > 0 in Ω u = 0 on ∂Ω, where Ω ⊂ R^2 is a smooth bounded domain and p > 1 is sufficiently large. Improving some known asymptotic estimates on the solutions, we prove the non-degeneracy and local uniqueness of the multi-spikes positive solutions for general domains. Our methods mainly use ODE’s theory, various local Pohozaev identities, blow-up analysis and the properties of Green’s function.
2022
Lane-Emden problem, asymptotic behavior, non-degeneracy, uniqueness
01 Pubblicazione su rivista::01a Articolo in rivista
Non-degeneracy and local uniqueness of positive solutions to the Lane-Emden problem in dimension two / Grossi, Massimo; Ianni, Isabella; Luo, Peng; Yan, Shusen. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 1776-3371. - 157(2022), pp. 145-210.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1605269
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