Almost Periodic Solutions of the Differential Equation in Locally Convex Spaces

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

Chapter Chapter 11 in Almost Periodic and Almost Automorphic Functions in Abstract Spaces, 2021, pp 125-128 from Springer

Abstract: Abstract As an application of results obtained in Chap. 3 , we will study conditions for almost periodicity of solutions of the linear differential equation x ′ ( t ) = A x ( t ) + f ( t ) , t ∈ ℝ $$x'(t)=Ax(t)+f(t),\;t\in \mathbb R$$ and the associated homogeneous equation in locally convex spaces. We will start with the case of a bounded linear operator A and then study the general case of a (eventually unbounded) linear operator A, which generates an equicontinuous C 0-semigroup of linear operators.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-73718-4_11

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DOI: 10.1007/978-3-030-73718-4_11

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