Liouville type results for the fractional truncated Laplacians in a half-space

Existence issues of viscosity supersolutions in the half-space ${\mathbb{R}}_{+}^N$, for a class of fully nonlinear integral equations involving the fractional truncated Laplacians and a power-like nonlinearity in the unknown function, are addressed in this paper, the aim being to obtain estimates on the threshold exponents separating the existence from the nonexistence regimes.