文章基本信息

标题：Stability of abstract dynamic equations on time scales
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作者：Alaa E Hamza ; Karima M Oraby
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2012
卷号：2012
期号：1
页码：143
DOI：10.1186/1687-1847-2012-143
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we investigate many types of stability, like uniform stability, asymptotic stability, uniform asymptotic stability, global stability, global asymptotic stability, exponential stability, uniform exponential stability, of the homogeneous first-order linear dynamic equations of the form x Δ ( t ) = A x ( t ) , t > t 0 , t , t 0 ∈ T x ( t 0 ) = x 0 ∈ D ( A ) , where A is the generator of a C 0 -semigroup { T ( t ) : t ∈ T } ⊂ L ( X ) , the space of all bounded linear operators from a Banach space X into itself. Here, T ⊆ R ≥ 0 is a time scale which is an additive semigroup with the property that a − b ∈ T for any a , b ∈ T such that a > b . Finally, we give an illustrative example for a nonregressive homogeneous first-order linear dynamic equation and we investigate its stability.
关键词：Dynamic Equation ; Asymptotic Stability ; Exponential Stability ; Global Asymptotic Stability ; Jump Operator