  In this paper, we aim to study solutions of reflected generalized BSDEs,
involving the integral with respect to a continuous process, which is the local
time of the diffusion on the boundary. We consider both a finite random
terminal and a infinite horizon. In both case, we establish an existence and
uniqueness result. Next, as an application, we get an American pricing option
in infinite horizon and we give a probabilistic formula for the viscosity
solution of an obstacle problem for elliptic PDEs with a nonlinear Neumann
boundary condition.
