Liouville-type theorems for fractional Hardy–Hénon systems

Abstract

In this paper, we study Liouville-type theorems for fractional Hardy–Hénon elliptic systems with weights. Because the weights are singular at zero, we firstly prove that classical solutions for systems in \({\mathbb {R}}^N \backslash \{0\}\) are also distributional solutions in \({\mathbb {R}}^N\). Then we study the equivalence between the fractional Hardy–Hénon system and a proper integral system, and we obtain new Liouville-type theorems for supersolutions and solutions by the method of integral estimates and scaling spheres respectively.