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arXiv · 1908.11122

Non-degeneracy for the critical Lane-Emden system

Rupert L. Frank·Seunghyeok Kim·Angela Pistoia
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Abstract

We prove the non-degeneracy for the critical Lane--Emden system $$ -\Delta U = V^p,\quad -\Delta V = U^q,\quad U, V > 0 \quad \text{in } \mathbb{R}^N $$ for all $N \ge 3$ and $p,q > 0$ such that $\frac{1}{p+1} + \frac{1}{q+1} = \frac{N-2}{N}$. We show that all solutions to the linearized system around a ground state must arise from the symmetries of the critical Lane-Emden system provided that they belong to the corresponding energy space or they decay to 0 uniformly as the point tends to infinity.

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Rupert L. Frank, Seunghyeok Kim, Angela Pistoia. 2019-08-29. Non-degeneracy for the critical Lane-Emden system. https://arxiv.org/abs/1908.11122

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