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Liouville theorems for fractional Hénon equation and system on $\mathbb{R}^n$

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  • In this paper, we establish some Liouville type theorems for positive solutions of fractional Hénon equation and system in $\mathbb{R}^n$. First, under some regularity conditions, we show that the above equation and system are equivalent to the some integral equation and system, respectively. Then, we prove Liouville type theorems via the method of moving planes in integral forms.
    Mathematics Subject Classification: Primary: 35B53; Secondary: 35B06.


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