Admissibility and roughness of nonuniform exponential dichotomies for difference equations

作者：Zhou, Linfeng; Zhang, Weinian^*

来源：Journal of Functional Analysis, 2016, 271(5): 1087-1129.

DOI：10.1016/j.jfa.2016.06.005

• Nonautonomous difference equations
• Nonuniform exponential dichotomy
• Admissibility
• Roughness

In this paper we discuss on relationships between nonuniform exponential dichotomies of nonautonomous difference equations and admissibility for classes of weighted bounded solutions and show the roughness of nonuniform exponential dichotomies in the finite dimensional case. We give sufficient conditions for existence of nonuniform exponential dichotomies on Z(0)(+) or Z(0)(-) separately, on Z(0)(+) and Z(0)(-) simultaneously and on the whole Z. As an application, we use this result to discuss the roughness of nonuniform exponential dichotomies for difference equations on Z(0)(+), Z(0)(-), and the whole Z separately and obtain better estimates for both the bound and the nonuniformity degree.

• 出版日期2016-9-1
• 单位四川大学