In this article, the existence of a unique solution in the variational
approach of the stochastic evolution equation \dX(t) = F(X(t)) \dt + G(X(t))
\dL(t) driven by a cylindrical L\'evy process L is established. The
coefficients F and G are assumed to satisfy the usual monotonicity and
coercivity conditions. The noise is modelled by a cylindrical L\'evy processes
which is assumed to belong to a certain subclass of cylindrical L\'evy
processes and may not have finite moments.Comment: Completely revised version, removed some inconsistencies and
inaccuracie