Uniqueness of non-linear ground states for fractional Laplacians in ℝ

Abstract

We prove uniqueness of ground state solutions Q = Q({pipe}x{pipe}) ≥ 0 of the non-linear equation (-Δ)s Q+Q-Qα+1= 0 in ℝ,(-Δ)s Q + Q - Q α + = 0 in ℝ where 0 < s < 1 and 0 < α < 4s/(1-2s) for s < 1/2 s < and 0 < α