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- W3039344944 abstract "We develop a monotonicity formula for solutions of the fractional Toda system $$ (-Delta)^s f_alpha = e^{-(f_{alpha+1}-f_alpha)} - e^{-(f_alpha-f_{alpha-1})} quad text{in} mathbb R^n,$$ when $0<s<1$, $alpha=1,cdots,Q$, $f_0=-infty$, $f_{Q+1}=infty$ and $Q ge2$ is the number of equations in this system. We then apply this formula, technical integral estimates, classification of stable homogeneous solutions, and blow-down analysis arguments to establish Liouville type theorems for finite Morse index (and stable) solutions of the above system when $n > 2s$ and $$ dfrac{Gamma(frac{n}{2})Gamma(1+s)}{Gamma(frac{n-2s}{2})} frac{Q(Q-1)}{2} > frac{ Gamma(frac{n+2s}{4})^2 }{ Gamma(frac{n-2s}{4})^2} . $$ Here, $Gamma$ is the Gamma function. When $Q=2$, the above equation is the classical (fractional) Gelfand-Liouville equation." @default.
- W3039344944 created "2020-07-10" @default.
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- W3039344944 creator A5065904836 @default.
- W3039344944 date "2020-06-30" @default.
- W3039344944 modified "2023-09-27" @default.
- W3039344944 title "On stable and finite Morse index solutions of the fractional Toda system" @default.
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- W3039344944 doi "https://doi.org/10.48550/arxiv.2007.00069" @default.
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