  We construct spherically symmetric, static solutions to the Einstein-Vlasov
system with non-vanishing cosmological constant $\Lambda$. The results are
divided as follows. For small $\Lambda>0$ we show existence of globally regular
solutions which coincide with the Schwarzschild-deSitter solution in the
exterior of the matter sources. For $\Lambda<0$ we show via an energy estimate
the existence of globally regular solutions which coincide with the
Schwarzschild-Anti-deSitter solution in the exterior vacuum region. We also
construct solutions with a Schwarzschild singularity at the center regardless
of the sign of $\Lambda$. For all solutions considered, the energy density and
the pressure components have bounded support. Finally, we point out a
straightforward method to obtain a large class of globally non-vacuum
spacetimes with topologies $\mathbb R\times S^3$ and $\mathbb R\times S^2\times
\mathbb R$ which arise from our solutions using the periodicity of the
Schwarzschild-deSitter solution. A subclass of these solutions contains black
holes of different masses.
