Existence and structure of solutions for a class of optimal control systems with discounting arising in economic dynamics

We study the existence and a turnpike property of solutions of a discrete-time control system with discounting and with a compact metric space of states. In our recent work for this discrete-time optimal control system without discounting we establish the turnpike property and show that it is stable under perturbations of an objective function. In the present paper we show that this turnpike property together with its stability also hold for the system with discounting.