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The objective of this article is to show a representation theorem for generators of backward stochastic differential equations via  L p( p  &gt; 1) solutions in general time intervals when the generatorsatisfies a monotonicity condition and a polynomial growth condition in  y  and a Lipschitz condition in  z  both non-uniformly with respect to  t . As its application, the corresponding converse comparison theorem for  L p( p  &gt; 1) solutions is obtained by this representation theorem.

Representation theorems of monotonicity generators for BSDEs via L p ( p > 1) solutions in general time intervals