scholarly journals On the Bohr transform of almost-periodic solutions for some differential equations in abstract spaces

2001 ◽  
Vol 27 (9) ◽  
pp. 521-534 ◽  
Author(s):  
Samuel Zaidman
Keyword(s):  
Linear Operator ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Banach Spaces ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Abstract Differential Equations ◽  
Abstract Spaces

We consider abstract differential equations of the formu′(t)=Au(t)+f(t)oru″(t)=Au(t)+f(t)in Banach spacesX, wheref(⋅),ℝ→Xis almost-periodic, whileAis a linear operator,𝒟(A)⊂X→X. If the solutionu(⋅)is likewise almost-periodic,ℝ→X, we establish connections between their Bohr-transforms,uˆ(λ)andfˆ(λ).

scholarly journals Eberlein weak almost periodic solutions for a class of integro-differential equations with infinite delay

2018 ◽  
Vol 5 (1) ◽  
pp. 127-137
Author(s):  
Khalil Ezzinbi ◽  
Samir Fatajou ◽  
Fatima Zohra Elamrani
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Weakly Almost Periodic

AbstractIn thiswork,we provide sufficient conditions ensuring the existence and uniqueness of an Eberlein weakly almost periodic solutions for some semilinear integro-differential equations with infinite delay in Banach spaces. For illustration, we provide an example arising in viscoelasticity theory.

scholarly journals WEIGHTED PSEUDO-ALMOST PERIODIC SOLUTIONS FOR SOME ABSTRACT DIFFERENTIAL EQUATIONS WITH UNIFORM CONTINUITY

2010 ◽  
Vol 82 (3) ◽  
pp. 424-436 ◽  
Author(s):  
LI-LI ZHANG ◽  
HONG-XU LI
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Uniform Continuity ◽  
Continuity Condition ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Abstract Differential Equations ◽  
Pseudo Almost Periodic Solutions ◽  
Pseudo Almost Periodic ◽  
Composition Theorem

AbstractIn this work, we give some theorems on (mild) weighted pseudo-almost periodic solutions for some abstract semilinear differential equations with uniform continuity. To facilitate this we give a new composition theorem of weighted pseudo-almost periodic functions. Our composition theorem improves the known one by making use of a uniform continuity condition instead of the Lipschitz condition.

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