  We consider exterior elliptic problems with coefficients stabilizing at
infinity and study the critical value $\beta_{cr}$ of the coupling constant
(the coefficient at the potential) that separates operators with a discrete
spectrum and those without it. The dependence of $\beta_{cr}$ on the boundary
condition and on the distance between the boundary and the support of the
potential is described. The discrete spectrum of a non-symmetric operator with
the FKW boundary condition (that appears in diffusion processes with traps) is
also investigated.
