  In this paper, we are interested in solving general time interval
multidimensional backward stochastic differential equations in $L^p$ $(p\geq
1)$. We first study the existence and uniqueness for $L^p$ $(p>1)$ solutions by
the method of convolution and weak convergence when the generator is monotonic
in $y$ and Lipschitz continuous in $z$ both non-uniformly with respect to $t$.
Then we obtain the existence and uniqueness for $L^1$ solutions with an
additional assumption that the generator has a sublinear growth in $z$
non-uniformly with respect to $t$.
