  We study a class of nonlocal reaction-diffusion equations with a harvesting
term where the nonlocal operator is given by a Bernstein function of the
Laplacian. In particular, it includes the fractional Laplacian, fractional
relativistic operators, sum of fractional Laplacians of different order etc. We
study existence, uniqueness and multiplicity results of the solutions to the
steady state equation. We also consider the parabolic counterpart and establish
the long time asymptotic of the solutions. Our proof techniques rely on both
analytic and probabilistic arguments.
