Liouville property of fractional Lane-Emden equation in general unbounded domain

Our purpose of this paper is to consider Liouville property for the fractional Lane-Emden equation (-Delta)(alpha)u = u(p) in Omega, u = 0 in R-N \ Omega, where alpha is an element of (0, 1), N >= 1, p > 0 and Omega subset of R-N-(1) x [0, +infinity) is an unbounded domain satisfying that Omega(t) := {x' is an element of RN-1 : (x', t) is an element of Omega} with t >= 0 has increasing monotonicity, that is, Omega(t) subset of Omega(t), for t' >= t. The shape of Omega(infinity):= lim(t ->infinity) Omega(t) in R-N-(1) plays an important role to obtain the nonexistence of positive solutions for the fractional Lane-Emden equation.