For a sequence of bounded linear operator {A_n}_n^∞=0 on a Banach space X, we investigate the characterization of exponential dichotomy of the difference equations v_n+1 = A_nv_n. We characterize the exponential dichotomy of difference equations in terms of the existence of solutions to the equations v_n+1 = A_nv_n + f_n in l_∞ space. Then we apply the result to study the exponential dichotomy of evolution families generated by evolution equations. © 2001 Elsevier Science Ltd.

Huy N.T., Van Minh N.

Gửi cho bạn bè

Từ khóa : Asymptotic stability; Evolutionary algorithms; Mathematical operators; Stability criteria; Theorem proving; Exponential dichotomy; Difference equations