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

作者：Grossi, Massimo^*; Ianni, Isabella; Luo, Peng; Yan, Shusen

来源：Journal des Mathematiques Pures et Appliquees, 2022, 157: 145-210.

DOI：10.1016/j.matpur.2021.10.001

• Lane-Emden problem
• Asymptotic behavior
• Non-degeneracy
• Uniqueness

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.

• 单位
  i; 5