The Equation x’(t)=A(t)x(t)+f(t)

Gaston M. N’Guérékata
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Gaston M. N’Guérékata: Morgan State University, Department of Mathematics

Chapter Chapter 10 in Almost Periodic and Almost Automorphic Functions in Abstract Spaces, 2021, pp 111-123 from Springer

Abstract: Abstract Case I. Let us first assume that 𝕏 $$\mathbb X$$ is of finite dimension, say 𝕏 = ℂ n $$\mathbb X = \mathbb C^n$$ . Let us consider the inhomogeneous linear evolution equations of the form d x ( t ) d t = A ( t ) x ( t ) + f ( t ) , t ∈ ℝ , x ( t ) ∈ 𝕏 , $$\displaystyle {\frac {dx(t)}{dt}}=A(t)x(t)+f(t), \quad t\in \mathbb R ,\; x(t) \in \mathbb X , $$ where A(⋅) is a τ-periodic (unbounded) linear operator-valued function and f ∈ A A ( 𝕏 ) $$f\in AA(\mathbb X)$$ .

Date: 2021
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DOI: 10.1007/978-3-030-73718-4_10

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