On a linear operator connected with almost periodic solutions of linear differential equations in Banach spaces

1967 ◽  
Vol 172 (4) ◽  
pp. 327-335 ◽  
Author(s):  
W. M. Bogdanowicz ◽  
J. N. Welch
Keyword(s):  
Linear Operator ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Banach Spaces ◽  
Linear Differential Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Linear Differential

scholarly journals On linear almost periodic systems with bounded solutions

1997 ◽  
Vol 55 (2) ◽  
pp. 177-184 ◽  
Author(s):  
V. I. Tkachenko
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Linear Differential Equations ◽  
Periodic Systems ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Bounded Solutions ◽  
Adjoint Matrix ◽  
Frequency Module ◽  
Linear Differential

It is proved that in every neighbourhood of a system of linear differential equations with almost periodic skew-adjoint matrix with frequency module ℱ there exists a system with frequency module contained in the rational hull of ℱ possessing all almost periodic solutions.

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).

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