We provide existence, comparison and stability results for one- dimensional backward stochastic differential equations (BSDEs) when the coefficient (or generator) $F(t,Y, Z)$ is continuous and has a quadratic growth in $Z$ and the terminal condition is bounded.e also give, in this framework, the links between the solutions of BSDEs set on a diffusion and viscosity or Sobolev solutions of the corresponding semilinear partial differential equations.
"Backward stochastic differential equations and partial differential equations with quadratic growth." Ann. Probab. 28 (2) 558 - 602, April 2000. https://doi.org/10.1214/aop/1019160253