Bounded solutions of nonlinear difference equatioris with advanced arguments
Sufficient conditions of existence and uniqueness of alpha-bounded and bounded solutions to the difference equation with advanced arguments x(n + 1) = A(n)x(n) + B(n)x(sigma(1)(n)) + f(n,x(n),x(sigma(2)(n))), sigma(i)(n) greater than or equal to n + 1, i = 1,2, are given. It is proven that under certain conditions it is possible to find positive numbers R, mu, such that from every initial condition satisfying \xi\ less than or equal to R, a unique bounded solution, belonging to the ball \x\ less than or equal to mu, starts. (C) 2003 Elsevier Science Ltd. All rights reserved.
bounded solutions existence uniqueness difference equations with advanced arguments