L1 solutions of multidimensional BSDEs with generators of time-varying one-sided Osgood type

In this paper, we establish existence and uniqueness of the L1 solution for general time interval multidimensional backward stochastic differential equations by virtue of the stopping time technique, Holder's inequality and Bihari's inequality,where the generator g satisfies a time-varying one-sided Osgood condition in y and a time-varying Lipschitz condition in z. This improves some existing results.