Nonlinear discrete systems with global boundary conditions

AbstractThis 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)=fk,x(k)+h(k),k=0,1,2,…, subject to constraints or nonlocal boundary conditions of the form ∑k=0∞gk,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)=fλ,k,x(k),k=0,1,2,…, subject to ∑k=0∞gλ,k,x(k)=0. We place particular importance on the behavior of the solutions as a function of the parameter λ