  We prove the existence of solutions to the asymptotic Plateau problem for
hypersurfaces of prescribed mean curvature in Cartan-Hadamard manifolds $N$.
More precisely, given a suitable subset $L$ of the asymptotic boundary of $N$
and a suitable function $H$ on $N$, we are able to construct a set of locally
finite perimeter whose boundary has generalized mean curvature $H$ provided
that $N$ satisfies the so-called strict convexity condition and that its
sectional curvatures are bounded from above by a negative constant. We also
obtain a multiplicity result in low dimensions.
