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This article is interested insolutions of general time interval backward stochastic differential equations (BSDEs) with generator  g  satisfying a  p -order weak stochastic-monotonicity condition and a general growth condition in  y . An existence and uniqueness result of the  L psolution is proved for the multidimensional BSDEs where the generator  g  is stochastic-Lipschitz in  z . And, a general comparison theorem and an existence and uniqueness theorem of the  L psolution is established for the one-dimensional BSDEs under a stochastic uniform-continuity condition of the generator  g  in  z . These results strengthen some known works. The stochastic Gronwall-type inequality and the stochastic Bihari-type inequality play an important role in the whole article.

L p solutions of general time interval BSDEs with generators satisfying a p -order weak stochastic-monotonicity condition