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

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.

Automated summary

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.