  We study a ground state of a non local Schrodinger operator associated with
an evolution equation for the density of population in the stochastic contact
model in continuum with inhomogeneous mortality rates. We found a new effect in
this model, when even in the high dimensional case the existence of a small
positive perturbation of a special form (so-called, small paradise) implies the
appearance of the ground state. We consider the problem in the Banach space of
bounded continuous functions $C_b (R^d)$ and in the Hilbert space $L^2(R^d)$.
