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

Abstract Existence issues of viscosity supersolutions in the half-space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> <mml:mi>N</mml:mi> </mml:msubsup> </mml:mrow> </mml:math> , 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.