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The objective of this paper is solving multidimensional backward stochastic differential equations with general time intervals, in $L^p$ $(p\geq 1)$ sense, where the generator $g$ satisfies a time-varying Osgood condition in $y$, a time-varying quasi-H\"older continuity condition in $z$, and its $i$th component depends on the $i$th row of $z$. Our result strengthens some existing works even for the case of finite time intervals.
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