  We prove the existence of weak solution for a system of quasi-variational
inequalities related to a switching problem with dynamic driven by operator
associated with a semi-Dirichlet form and with measure data. We give a
stochastic representation of solutions in terms of solutions of a system of
reflected BSDEs with oblique reflection. As a by-product, we prove the
existence of an optimal strategy in the switching problem and show regularity
of the payoff function.
