  This paper deals with existence and uniqueness, in viscosity sense, of a
solution for a system of m variational partial differential inequalities with
inter-connected obstacles. A particular case of this system is the
deterministic version of the Verification Theorem of the Markovian optimal
m-states switching problem. The switching cost functions are arbitrary. This
problem is connected with the valuation of a power plant in the energy market.
The main tool is the notion of systems of reflected BSDEs with oblique
reflection.
