  In this paper, by introducing a new notion of envelope of the stochastic
process, we construct a family of random differential equations whose solutions
can be viewed as solutions of a family of ordinary differential equations and
prove that the multidimensional backward stochastic differential equations
(BSDEs for short) with the general uniformly continuous coefficients are
uniquely solvable. As a result, we solve the open problem of multidimensional
BSDEs with uniformly continuous coefficients.
