In this paper we consider two classes of backward stochastic differential
equations. Firstly, under a Lipschitz-type condition on the generator of the
equation, which can also be unbounded, we give sufficient conditions for the
existence of a unique solution pair. The method of proof is that of Picard
iterations and the resulting conditions are new. We also prove a comparison
theorem. Secondly, under the linear growth and continuity assumptions on the
possibly unbounded generator, we prove the existence of the solution pair. This
class of equations is more general than the existing ones
