  In this paper, we study a functional fully coupled forward-backward
stochastic differential equations (FBSDEs). Under a new type of integral
Lipschitz and monotonicity conditions, the existence and uniqueness of
solutions for functional fully coupled FBSDEs is proved. We also investigate
the relationship between the solution of functional fully coupled FBSDE and the
classical solution of the path-dependent partial differential equation (P-PDE).
When the solution of the P-PDE has some smooth and regular properties, we solve
the related functional fully coupled FBSDE and prove the P-PDE has a unique
solution.
