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arXiv · 1911.09000

Liouville type theorems for fractional and higher-order fractional H\'enon-Lane-Emden systems

Daomin Cao·Guolin Qin
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Abstract

In this paper, we first establish decay estimates for the fractional and higher-order fractional H\'enon-Lane-Emden systems by using a nonlocal average and integral estimates, which deduce a result of non-existence. Next, we apply the method of scaling spheres introduced in \cite{DQ2} to derive a Liouville type theorem. We also construct an interesting example on super $\frac{\alpha}{2}$-harmonic functions (Proposition 1.2).

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Daomin Cao, Guolin Qin. 2019-11-20. Liouville type theorems for fractional and higher-order fractional H\'enon-Lane-Emden systems. https://doi.org/10.3934/dcds.2020361

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