LIOUVILLE TYPE THEOREMS FOR FRACTIONAL ELLIPTIC SYSTEMS WITH COUPLED TERMS.

In this paper, we study the fractional elliptic system with coupled terms {(-Δ)^su = (q+1)u^qv^p+1 in ℝ^N (-Δ)^su = (q+1)v^qu^p+1 in ℝ^N 0 < s < 1 and N > 2s. We first prove that if p > -1, q > -1 and p+q+1 ≤ N/N-2s, then the system has no positive supersolution. In the case p,q > 0 we establish the nonexistence result of stable positive solutions. Our results generalize some results in [Li, Yayun; Lei, Yutian; Commun. Pure Appl. Anal. 17 (2018), no. 5, 1749-1764.] to the system involving the fractional Laplacian. [ABSTRACT FROM AUTHOR]