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<fen><cp type="lpar" STYLE="S">k,x(k)<cp type="rpar" STYLE="S"></fen>+h(k), k=0,1,2,…, subject to constraints or nonlocal boundary conditions of the form ∑lower limit k=0, upper limit ∞ g<fen><cp type="lpar" STYLE="S">k,x(k)<cp type="rpar" STYLE="S"></fen>=y we analyze how perturbations in <f>h</f> and <f>y</f> affect the existence of <f>l∞</f>-solutions of this problem. In this setting, <f>h</f> is an element of <f>l∞</f> and <f>y</f> belongs to <f>Rp</f>. We also study the existence and behavior of bounded solutions to problems of the form x(k+1)=f<fen><cp type="lpar" STYLE="S">λ,k,x(k)<cp type="rpar" STYLE="S"></fen>, k=0,1,2,…, subject to ∑lower limit k=0, upper limit ∞ g<fen><cp type="lpar" STYLE="S">λ,k,x(k)<cp type="rpar" STYLE="S"></fen>=0. We place particular importance on the behavior of the solutions as a function of the parameter <f>λ</f>. [Copyright &y& Elsevier]