  We present the extension of the Einstein-Maxwell system called electrovac
universes by introducing a cosmological constant $\Lambda$. In the absence of
the $\Lambda$ term, the crucial equation in solving the Einstein-Maxwell system
is the Laplace equation. The cosmological constant modifies this equation to
become in a non-linear partial differential equation which takes the form
$\Delta U=2\Lambda U^3$. We offer special solutions of this equation.
