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arXiv · 2003.03071

Classification of stable solutions to a non-local Gelfand-Liouville equation

Ali Hyder·Wen Yang
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Abstract

We study finite Morse index solutions to the non-local Gelfand-Liouville problem $$ (-\Delta)^su=e^u\quad\mathrm{in}\quad \mathbb{R}^n,$$ for every $s\in(0,1)$ and $n>2s$. Precisely, we prove non-existence of finite Morse index solutions whenever the singular solution $$u_{n,s}(x)=-2s\log|x|+\log \left(2^{2s}\frac{\Gamma(\frac{n}{2})\Gamma(1+s)}{\Gamma(\frac{n-2s}{2})}\right)$$ is unstable.

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Ali Hyder, Wen Yang. 2020-03-06. Classification of stable solutions to a non-local Gelfand-Liouville equation. https://arxiv.org/abs/2003.03071

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