In this paper, we study the backward stochastic differential equations driven by G-Brownian motion under the condition that the generator is time-varying Lipschitz continuous with respect to y and time-varying uniformly continuous with respect to z. With the help of linearization method and the G-stochastic analysis techniques, we construct the approximating sequences of G-BSDE and obtain some precise a priori estimates. By combining this with the approximation method, we prove the existence and uniqueness of the solution under the time-varying conditions, as well as the comparison theorem.

翻译：本文研究了在生成元关于y具有时变Lipschitz连续性、关于z具有时变一致连续性条件下，由G-布朗运动驱动的倒向随机微分方程。借助线性化方法和G-随机分析技术，我们构造了G-BSDE的逼近序列，并得到了若干精确的先验估计。结合逼近方法，我们证明了在时变条件下解的存在唯一性，以及比较定理。