  We present a unified approach to $L^p$-solutions ($p > 1$) of
multidimensional backward stochastic differential equations (BSDEs) driven by
L\'evy processes and more general filtrations. New existence, uniqueness and
comparison results are obtained. The generator functions obey a time-dependent
extended monotonicity (Osgood) condition in the $y$-variable and have general
growth in $y$. Within this setting, the results generalize those of Royer
(2006), Yin and Mao (2008), Yao (2017), Kruse and Popier (2016/2017) and Geiss
and Steinicke (2018).
