  We study the problem of existence of solutions for generalized backward
stochastic differential equation with two reflecting barriers (GRBSDE for
short) under weaker assumptions on the data. Roughly speaking we show the
existence of a maximal solution for GRBSDE when the terminal condition \xi is
F_T-measurable, the coefficient f is continuous with general growth with
respect to the variable y and stochastic quadratic growth with respect to the
variable z and the reflecting barriers L and U are just right continuous left
limited. The result is proved without assuming any P-integrability conditions.
