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 $L^p$ $(p\geq 1)$ solutions of multidimensional BSDEs with time-varying quasi-H\"older continuity generators in general time intervals Commun. Korean Math. Soc.Published online January 30, 2020 Xiao Lishun and Fan Shengjun Xuzhou Medical University, China University of Mining and Technology Abstract : The objective of this paper is solving $L^p$ $(p\geq 1)$ solutions of multidimensional backward stochastic differential equations with general time intervals, 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 though for the case of finite time intervals. Keywords : Backward stochastic differential equation; $L^p$ $(p\geq 1)$ solution; General time interval; Osgood condition; quasi-H\"older continuity MSC numbers : 60H10 Full-Text :