Pseudo-almost periodicity of some nonautonomous evolution equations with delay

2007 ◽  
Vol 67 (5) ◽  
pp. 1412-1418 ◽  
Author(s):  
Hui-Sheng Ding ◽  
Jin Liang ◽  
Gaston M. N’Guérékata ◽  
Ti-Jun Xiao
Keyword(s):  
Evolution Equations ◽  
Almost Periodicity ◽  
Pseudo Almost Periodicity ◽  
Equations With Delay

scholarly journals Stepanov-like pseudo almost periodic functions on time scales and applications to dynamic equations with delay

2018 ◽  
Vol 16 (1) ◽  
pp. 826-841 ◽  
Author(s):  
Chao-Hong Tang ◽  
Hong-Xu Li
Keyword(s):  
Time Scales ◽  
Dynamic Equations ◽  
Translation Invariance ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Pseudo Almost Periodicity ◽  
Pseudo Almost Periodic ◽  
Equations With Delay

AbstractIn this paper, we introduce the concept of Sp-pseudo almost periodicity on time scales and present some basic properties of it, including the translation invariance, uniqueness of decomposition, completeness and composition theorem. Moreover, we prove the seemingly simple but nontrivial result that pseudo almost periodicity implies Stepanov-like pseudo almost periodicity. As an application of the abstract results, we present some existence and uniqueness results on the pseudo almost periodic solutions of dynamic equations with delay.

scholarly journals (ω, c)- Pseudo almost periodic distributions

2020 ◽  
Vol 7 (1) ◽  
pp. 237-248 ◽  
Author(s):  
Mohammed Taha Khalladi ◽  
Abdelkader Rahmani
Keyword(s):  
Almost Periodicity ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Differential Systems ◽  
Schwartz Distributions ◽  
Pseudo Almost Periodic Solutions ◽  
Linear Differential Systems ◽  
Linear Differential ◽  
Pseudo Almost Periodicity ◽  
Pseudo Almost Periodic

AbstractThe paper is a study of the (w, c) −pseudo almost periodicity in the setting of Sobolev-Schwartz distributions. We introduce the space of (w, c) −pseudo almost periodic distributions and give their principal properties. Some results about the existence of distributional (w, c) −pseudo almost periodic solutions of linear differential systems are proposed.

Asymptotic Almost Periodicity to Some Evolution Equations

2015 ◽  
Vol 34 (4) ◽  
pp. 459-475
Author(s):  
Rong-Nian Wang ◽  
Qiao-Min Xiang ◽  
Yong Zhou
Keyword(s):  
Evolution Equations ◽  
Almost Periodicity

scholarly journals A Class of Fractional Degenerate Evolution Equations with Delay

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1700
Author(s):  
Amar Debbouche ◽  
Vladimir E. Fedorov
Keyword(s):  
Unique Solvability ◽  
Evolution Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Systems Of Equations ◽  
Fractional Differential ◽  
Initial Boundary Value ◽  
Degenerate Type ◽  
Degenerate Evolution Equations ◽  
Equations With Delay

We establish a class of degenerate fractional differential equations involving delay arguments in Banach spaces. The system endowed by a given background and the generalized Showalter–Sidorov conditions which are natural for degenerate type equations. We prove the results of local unique solvability by using, mainly, the method of contraction mappings. The obtained theory via its abstract results is applied to the research of initial-boundary value problems for both Scott–Blair and modified Sobolev systems of equations with delays.

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