  In this study, we concern the multidimensional viscosity solutions theory of
a kind of semi-linear partial differential equations (PDEs). A new definition
of viscosity solution for this multidimensional semi-linear PDEs which is
related to a type of multidimensional backward stochastic differential
equations (BSDEs) is given. Further more, we establish the existence and
uniqueness results for the viscosity solution of this semi-linear PDEs via the
comparison theorem of the related BSDEs and a smooth approximation technique.
