Fractional p-Laplacian problems with negative powers in a ball or an exterior domain

This paper is concerned with the qualitative properties of positive solutions to fractional p-Laplacian problems

in , where 0 < s < 1, p ≥ 2, q > 0, α ≥ 0 and B₁ is the unit ball centered at the origin. By deriving a decay at infinity principle and exploiting the direct method of moving planes for the fractional p-Laplacian, we prove the symmetry or monotonicity of positive solutions to the above problems.