A Liouville type theorem for polyharmonic elliptic systems

In this paper, we consider the polyharmonic system (− )mU = V q, (− )mV = Up in RN, for m>1, N >2m, with p 1, q 1, but not both equal to 1, where (− )m is the polyharmonic operator. Set α = 2m(q +1)/(pq −1), β = 2m(p+1)/(pq −1), for α,β ∈ [(N −2)/2,N −2m), we prove the nonexistence of positive solutions. © 2006 Elsevier Inc. All rights reserved.