Admissibility and roughness of nonuniform exponential dichotomies for difference equations

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• 作者：Linfeng Zhou ; Weinian Zhang ; ^{matzwn@126.com" class="auth_mail" title="E-mail the corresponding author} ; ^{wnzhang@scu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：34D09 ; 37D25 ; 39A06
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：1 September 2016
• 年：2016
• 卷：271
• 期：5
• 页码：1087-1129
• 全文大小：648 K

文摘

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 ${\mathbb{Z}}_0^{+}$ or ${\mathbb{Z}}_0^{-}$ separately, on ${\mathbb{Z}}_0^{+}$ and ${\mathbb{Z}}_0^{-}$ simultaneously and on the whole Z$\mathbb{Z}$. As an application, we use this result to discuss the roughness of nonuniform exponential dichotomies for difference equations on ${\mathbb{Z}}_0^{+}$, ${\mathbb{Z}}_0^{-}$ and the whole Z$\mathbb{Z}$ separately and obtain better estimates for both the bound and the nonuniformity degree.