scholarly journals Asymptotic stability of a perturbed abstract differential equations in Banach spaces

2020 ◽  
pp. 129-138
Author(s):  
Hanen Damak ◽  
Mohamed Ali Hammami
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Banach Spaces ◽  
Abstract Differential Equations

scholarly journals Robustness with respect to small delays for exponential stability of abstract differential equations in Banach spaces

2006 ◽  
Vol 47 (4) ◽  
pp. 555-568 ◽  
Author(s):  
Faming Guo ◽  
Bin Tang ◽  
Falun Huang
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Banach Spaces ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Operator Family ◽  
Abstract Differential Equations ◽  
Fundamental Operator ◽  
Square Integrability ◽  
Necessary And Sufficient

AbstractThis paper is concerned with robustness with respect to small delays for the exponential stability of abstract differential equations in Banach spaces. Some necessary and sufficient conditions are given in terms of the uniformly square integrability of the fundamental operator family and the uniform boundedness of its resolvent on the imaginary axis.

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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