Nonlinear discrete systems with global boundary conditions

This paper is devoted to the study of boundary value problems on infinite time intervals for nonlinear, discrete-time systems. For problems of the form x(k + 1) = f k, x(k) + h(k), k = 0, 1, 2, . . . , subject to constraints or nonlocal boundary conditions of the form ∞ k=0 g k, x(k) = y we analyze how perturbations in h and y affect the existence of l∞-solutions of this problem. In this setting, h is an element of l∞ and y belongs to Rp. We also study the existence and behavior of bounded solutions to problems of the form x(k + 1) = f λ, k, x(k) , k= 0, 1, 2, . . . , subject to ∞ k=0 g λ, k, x(k) = 0. We place particular importance on the behavior of the solutions as a function of the parameter λ.  2003 Elsevier Inc. All rights reserved.