Exponential dichotomy of difference equations and applications to evolution equations on the half-line

Abstract

For a sequence of bounded linear operator {An}n∞=0 on a Banach space X, we investigate the characterization of exponential dichotomy of the difference equations vn+1 = Anvn. We characterize the exponential dichotomy of difference equations in terms of the existence of solutions to the equations vn+1 = Anvn + fn in l∞ space. Then we apply the result to study the exponential dichotomy of evolution families generated by evolution equations. © 2001 Elsevier Science Ltd.