  We show existence and uniqueness of a continuous with polynomial growth
viscosity solution of a system of second order integral-partial differential
equations (IPDEs for short) without assuming the usual monotonicity condition
of the generator with respect to the jump component as in Barles et al.'s
article \cite{BarlesBuckPardoux}. The L\'evy measure is arbitrary and not
necessarily finite. In our study the main tool we used is the notion of
backward stochastic differential equations with jumps.
