Asymptotic Behavior of Linear and Almost Periodic Discrete Evolution Systems on Banach Space AAP(0)(r)(Z(+),W)

作者：Zada Akbar^*; Arif Muhammad; Khalid Habiba

来源：Qualitative Theory of Dynamical Systems, 2016, 15(2): 597-605.

DOI：10.1007/s12346-015-0177-5

• Difference evolution equations
• Uniform exponential stability
• Almost periodic sequences
• Banach Space

Let be the solution of the nonhomogeneous evolution difference equation , for all , where is a sequence of almost periodic (possibly unbounded) linear operators on a Banach space . Let is the space of all -valued bounded sequences which decays at zero and at infinity and is the space of all -valued almost periodic sequences decaying at zero. We consider the space consisting of all sequences with relatively compact ranges for which there exists and such that . We prove that belongs to if and only if for each the discrete evolution family of operators is uniformly exponentially stable. Our results are based on evolution semigroup approach.

• 出版日期2016-10