LAUSR

AbstractIn this paper, we study the Pohozaev identity associated with a H´enon–Lane–Emden system involving the fractional Laplacian: $$\left\{ {\begin{array}{*{20}{c}} {{{\left( { - \Delta } \right)}^s}u = {{\left| x \right|}^a}{v^p},}&{x \in \Omega ,} \\ {{{\left( { - \Delta } \right)}^s}u = {{\left| x \right|}^b}{v^q},}&{x \in \Omega ,} \\ {u = v = 0,}&{x \in {\mathbb{R}^n}\backslash \Omega ,} \end{array}} \right.$${(−Δ)su=|x|avp,x∈Ω,(−Δ)su=|x|bvq,x∈Ω,u=v=0,x∈ℝn\Ω, in a star-shaped and bounded domain Ω for s ∈ (0, 1). As an application of our identity, we deduce the nonexistence of positive solutions in the critical and supercritical cases.