  The question studied here is the existence and uniqueness of a non-trivial
bounded steady state of a Fisher-KPP equation involving a fractional Laplacian
(--$\Delta$)^$\alpha$ in a domain with Dirichlet conditions outside of the
domain. More specifically, we investigate such questions in the case of general
fragmented unbounded domains. Indeed, we take advantage of the non-local
dispersion in order to provide analytic bounds (which depend only on the
domain) on the steady states. Such results are relevant in biology. For
instance, our results provide criteria on the domain for the subsistence of a
species subject to a non-local diffusion in a fragmented area. These criteria
primarily involve the sign of the first eigenvalue of the operator
(--$\Delta$)^$\alpha$ -- Id in a domain with Dirichlet conditions outside of
the domain. To this end, we exhibit a result of continuity of this principal
eigenvalue with respect to the distance between two compact patchs in the one
dimensional case. The main novelty of this last result is the continuity up to
the distance 0.
