Weighted pseudo almost periodic functions and applications to evolution equations with delay

2013 ◽  
Vol 219 (17) ◽  
pp. 8949-8958 ◽  
Author(s):  
Hui-Sheng Ding ◽  
Jin Liang ◽  
Ti-Jun Xiao
Keyword(s):  
Evolution Equations ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Pseudo Almost Periodic Functions ◽  
Pseudo Almost Periodic ◽  
Equations With Delay

scholarly journals Weighted Pseudo Almost-Periodic Functions and Applications to Semilinear Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Jun Zhang ◽  
Ti-Jun Xiao ◽  
Jin Liang
Keyword(s):  
Existence Theorem ◽  
Evolution Equations ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Pseudo Almost Periodic Functions ◽  
Exponentially Stable ◽  
Pseudo Almost Periodic ◽  
Semilinear Evolution Equations ◽  
Composition Theorem

We first give a solution to a key problem concerning the completeness of the space of weighted pseudo almost-periodic functions and then establish a new composition theorem with respect to these functions. Some important remarks with concrete examples are also presented. Moreover, we prove an existence theorem for the weighted pseudo almost-periodic mild solution to the semilinear evolution equation:x′(t)=Ax(t)+f(t,x(t)),t∈ℝ, whereAis the infinitesimal generator of an exponentially stableC0-semigroup. An application is also given to illustrate the abstract existence theorem.

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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