  In a recent paper, Soner, Touzi and Zhang [20] have introduced a notion of
second order backward stochastic differential equations (2BSDEs for short),
which are naturally linked to a class of fully non-linear PDEs. They proved
existence and uniqueness for a generator which is uniformly Lipschitz in the
variables $y$ and $z$. The aim of this paper is to extend these results to the
case of a generator satisfying a monotonicity condition in $y$. More precisely,
we prove existence and uniqueness for 2BSDEs with a generator which is
Lipschitz in $z$ and uniformly continuous with linear growth in $y$. Moreover,
we emphasize throughout the paper the major difficulties and differences due to
the 2BSDE framework.
