| Abstract: |
| We present uniqueness results for non-negative solutions of semilinear equations with a power nonlinearity, set in bounded planar domains with Dirichlet boundary conditions.
The talk is mainly based on the following joint works:
[1] F. De Marchis, M. Grossi, I. Ianni, F. Pacella, Morse index and uniqueness of positive solutions of the Lane-Emden problem in planar domains, J. Math. Pures Appl. 128, 2019.
[2] M. Grossi, I. Ianni, P. Luo, S. Yan, Non-degeneracy and local uniqueness of positive solutions to the Lane-Emden problem in dimension two, J. Math. Pures Appl. 128, 2022.
[3] I. Ianni, P. Luo, S. Yan, Morse index, topological degree and local uniqueness of multi-spikes solutions to the Lane-Emden problem in dimension two, submitted |
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