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Liouville type theorems for fractional and higher-order fractional systems

D. Cao was supported by NNSF of China (No.11831009) and Chinese Academy of Sciences (No.QYZDJ-SSW-SYS021)

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  • In this paper, we first establish decay estimates for the fractional and higher-order fractional Hénon-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 [16] to derive a Liouville type theorem. We also construct an interesting example on super $ \frac{\alpha}{2} $-harmonic functions (Proposition 1.2).

    Mathematics Subject Classification: Primary: 35J61; Secondary: 35B53, 35C15.


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  • Figure 1.  Spherical coordinate system

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