Two-barriers-reflected generalized BSDE: A general result and application

We investigate generalized backward stochastic differential equations with two reflecting barriers. Under the conditions that the barriers are completely separated and the generators are monotone, we establish a general result regarding the existence and uniqueness of the solution. In the Markovian framework, this result is applied to prove the existence and uniqueness of the viscosity solution to an obstacle problem for a partial differential equation with nonlinear Neumann boundary conditions.