  The present paper is devoted to investigating the existence and uniqueness of
solutions to a class of non-Lipschitz scalar valued backward stochastic
differential equations driven by $G$-Brownian motion ($G$-BSDEs). In fact, when
the generators are Lipschitz continuous in $y$ and uniformly continuous in $z$,
we construct the unique solution to such equations by monotone convergence
argument. The comparison theorem and related Feynman-Kac formula are stated as
well.
