Solve a special non-linear Backward SDE It is straigtforward to solve a linear Backward SDE. i.e.
$dY_t=Z_tdW_t+ aY_tdt+bZ_tdt$ with $Y_T=\xi$ (where a  and b are constants, $\xi$ is bounded Randon Variable.)

How can I solve $dY_t=Z_tdW_t+ a(Y_t)^+dt +bZ_tdt $ with $Y_T=\xi$ ?

($(Y_t)^+$ means the positive part of $Y_t$)

This question is very important for me. I have got stucked in it for more than one week, after trying several methods. I will be very grateful if anyone can give me some hint about possible ways to solve it! Please, any suggestion is very important for me.

I am also interested in solving $dY_t=Z_tdW_t+ a(Y_t)^+dt +b(Z_t)^+dt $ with $Y_T=\xi$ ?

I am a starter in Backward SDE and wish to explore deeper in how to solve different BSDEs. Can anyone suggest me some related books?

Thank you so much!!
The easiest way is to assume Y is positive and solve it. If the solution is positive, then it is the actual solution. Another way is that if the BSDE is Markovian, you can solve the corresponding PDE(Feynman-Kac formula). In general, the solution should depend heavily in choosing $\xi$. Therefore, one may not get general solution for any $\xi$.
The easiest way is to assume Y is positive and solve it. If the solution is positive, then it is the actual solution. Another way is that if the BSDE is Markovian, you can solve the corresponding PDE(Feynman-Kac formula). In general, the solution should depend heavily in choosing $\xi$. Therefore, one may not get general solution for any $\xi$.