  We study the existence of stationary solutions for a nonlocal version of the
Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) equation. The main motivation is
a recent study by Berestycki et {al.} [Nonlinearity 22 (2009),
{pp.}~2813--2844] where the nonlocal FKPP equation has been studied and it was
shown for the spatial domain $\mathbb{R}$ andsufficiently small nonlocality
that there are only two bounded non-negative stationary solutions. Here we
provide a similar result for $\mathbb{R}^d$ using a completely different
approach. In particular, an abstract perturbation argument is used in suitable
weighted Sobolev spaces. One aim of the alternative strategy is that it can
eventually be generalized to obtain persistence results for hyperbolic
invariant sets for other nonlocal evolution equations on unbounded domains with
small nonlocality, {i.e.}, to improve our understanding in applications when a
small nonlocal influence alters the dynamics and when it does not.
