Non-degeneracy and local uniqueness of positive solutions to the Lane-Emden problem in dimension two
نویسندگان
چکیده
We are concerned with the Lane-Emden problem{−Δu=upinΩ,u>0inΩ,u=0on∂Ω, where Ω⊂R2 is a smooth bounded domain and p>1 sufficiently large. Improving some known asymptotic estimates on solutions, we prove non-degeneracy local uniqueness of multi-spikes positive solutions for general domains. Our methods mainly use ODE's theory, various Pohozaev identities, blow-up analysis properties Green's function. Nous sommes concernés par le problème de Lane-Emden{−Δu=updansΩ,u>0dansΩ,u=0sur∂Ω, où est un domaine borné et suffisamment grand. En améliorant certaines estimations asymptotiques connues sur les nous prouvons la non-dégénérescence l'unicité locale des positives à pointes multiples pour domaines généraux. Nos méthodes principalement utiliser théorie d'ODE, diverses identités locales Pohozaev, l'analyse explosions propriétés fonction Green.
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ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2022
ISSN: ['0021-7824', '1776-3371']
DOI: https://doi.org/10.1016/j.matpur.2021.10.001