Before revision:  The properties of locally Lipschitz BSDEs with coefficients in BMO space enable us to show the  strong convergence of a sequence of globally Lipschitz BSDEs to the interested one , which is then used to give sufficient conditions for the Malliavin's differentiability.
After revision:  The properties of locally Lipschitz BSDEs with coefficients in BMO space enable us to show the so-called A_gamma-condition for the comparison principle to hold, we prove the existence of a unique solution under the general quadratic-exponential structure. We have also shown that the strong convergence of a sequence of globally Lipschitz BSDEs to the interested one , which is then used to give sufficient conditions for the Malliavin's differentiability.