Liouville-type theorems for fractional Hardy–Hénon systems

Abstract

AbstractIn 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 $${\mathbb {R}}^N \backslash \{0\}$$ R N \ { 0 } are also distributional solutions in $${\mathbb {R}}^N$$ 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.