Asymptotically periodic solutions of abstract differential equations

作者：Henriquez Hernan R^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2013, 80: 135-149.

DOI：10.1016/j.na.2012.10.010

• S-asymptotically periodic functions
• Stepanov asymptotically periodic functions
• Abstract differential equations
• Semigroups of bounded linear operators

In this paper, we introduce the concept of S-asymptotically omega-periodicity in the Stepanov sense. We study some properties of the space consisting of S-asymptotically omega-periodic functions, and we use this notion to establish the existence of S-asymptotically omega-periodic solutions to linear and semi-linear first-order abstract differential equations. In particular, we characterize the strongly continuous semigroups of bounded linear operators defined on reflexive spaces which are S-asymptotically omega-periodic as those semigroups which are the direct sum of an omega-periodic and a strongly stable semigroup.

• 出版日期2013-3