Journal
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
Volume 157, Issue -, Pages 145-210Publisher
ELSEVIER
DOI: 10.1016/j.matpur.2021.10.001
Keywords
Lane-Emden problem; Asymptotic behavior; Non-degeneracy; Uniqueness
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Funding
- INDAM-GNAMPA
- INDAM-GNAMPA [PRIN 2017JPCAPN-003]
- VALERE project
- NNSF of China [12171183, 11831009, 12171184]
- China Scholarship Council [201906775030]
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This study focuses on the Lane-Emden problem, proving the non-degeneracy and local uniqueness of multi-spikes positive solutions for general domains. The methods utilized include ODE theory, various local Pohozaev identities, blow-up analysis, and the properties of Green's function.
We are concerned with the Lane-Emden problem {-Delta u = u(P)in Omega, u > 0 in Omega, u = 0 on partial derivative Omega, where Omega subset of 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. (C) 2021 Elsevier Masson SAS. All rights reserved.
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