scholarly journals Composition of piecewise pseudo almost periodic functions and applications to abstract impulsive differential equations

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Junwei Liu ◽  
Chuanyi Zhang
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Pseudo Almost Periodic Functions ◽  
Pseudo Almost Periodic

Piecewise weighted pseudo almost periodic functions and applications to impulsive differential equations

2016 ◽  
Vol 66 (5) ◽  
Author(s):  
Na Song ◽  
Hong-Xu Li ◽  
Chuan-Hua Chen
Keyword(s):  
Impulsive Differential Equation ◽  
Mild Solutions ◽  
Impulsive Differential Equations ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Pseudo Almost Periodic Functions ◽  
Essential Properties ◽  
Existence And Stability ◽  
Pseudo Almost Periodic

AbstractIn this paper, we introduce a concept of piecewise weighted pseudo almost periodic functions on a Banach space and present the essential properties of this kind of functions, including the composition theorems and the uniqueness of decomposition of the functions. As an application, we give some results on the existence and stability of piecewise weighted pseudo almost periodic mild solutions to an abstract impulsive differential equation. Moreover, a concrete example is given to illustrate our abstract results.

scholarly journals Some Properties of Weighted Pseudo almost Periodic Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhe-Ming Zheng ◽  
Hui-Sheng Ding ◽  
Gaston M. N’Guérékata
Keyword(s):  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Proper Subspace ◽  
Equivalent Definition ◽  
Classical Space ◽  
Pseudo Almost Periodic Functions ◽  
Close Relationship ◽  
Pseudo Almost Periodic ◽  
Asymptotically Almost Periodic

Several interesting and new properties of weighted pseudo almost periodic functions are established. Firstly, we obtain an equivalent definition for weighted pseudo almost periodic functions, which shows a close relationship between asymptotically almost periodic functions and weighted pseudo almost periodic functions; secondly, we prove that the space of asymptotically almost periodic functions is always a proper subspace of the space of weighted pseudo almost periodic functions; thirdly, we show that under some cases, the space of weighted pseudo almost periodic functions equals the classical space of pseudo almost periodic functions.

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