  We study the boundary value problem with Radon measures for nonnegative
solutions of $L_Vu:=-\Delta u+Vu=0$ in a bounded smooth domain $\Gw$, when $V$
is a locally bounded nonnegative function. Introducing some specific capacity,
we give sufficient conditions on a Radon measure $\gm$ on $\prt\Gw$ so that the
problem can be solved. We study the reduced measure associated to this equation
as well as the boundary trace of positive solutions. In the appendix A. Ancona
solves a question raised by M. Marcus and L. V\'eron concerning the vanishing
set of the Poisson kernel of $L_V$ for an important class of potentials $V$.
