论文标题
将稳定解决方案分类为非本地Gelfand-Liouville方程式
Classification of stable solutions to a non-local Gelfand-Liouville equation
论文作者
论文摘要
我们研究非本地Gelfand-Liouville问题的有限摩尔斯索引解决方案 $$（-Δ）^su = e^u \ quad \ mathrm {in} \ quad \ quad \ mathbb {r}^n，$ $ s \ in（0,1）$和$ n> 2s $。确切地说，每当单数解决方案$$ u_ {n，s}（x）= -2S \ log | x |+\ log时，我们证明有限摩尔斯索引解决方案不存在\ left（2^{2S} \ frac {γ（\ frac {n} {2}）γ（1+s）}} {γ（\ frac {n-2s} {2} {2} {2} {2} {2}} \ right）$$不稳定。
We study finite Morse index solutions to the non-local Gelfand-Liouville problem $$ (-Δ)^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{Γ(\frac{n}{2})Γ(1+s)}{Γ(\frac{n-2s}{2})}\right)$$ is unstable.
