Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties

María del Mar González, Mariel Sáez, Yannick Sire

We investigate the equation $$(-{\Delta }_{{\mathbb{H}}^n}{)}^{\gamma }w=f(w)in{\mathbb{H}}^n,$$ where $(-{\Delta }_{{\mathbb{H}}^n}{)}^{\gamma }$ corresponds to the fractional Laplacian on hyperbolic space for $γ\i…