A Liouville type theorem for polyharmonic elliptic systems

Abstract

In this paper, we consider the polyharmonic system ( − Δ ) m U = V q , ( − Δ ) m V = U p in R N , for m > 1 , N > 2 m , with p ⩾ 1 , q ⩾ 1 , but not both equal to 1, where ( − Δ ) m is the polyharmonic operator. Set α = 2 m ( q + 1 ) / ( p q − 1 ) , β = 2 m ( p + 1 ) / ( p q − 1 ) , for α , β ∈ [ ( N − 2 ) / 2 , N − 2 m ) , we prove the nonexistence of positive solutions.