Almost Periodic Solutions of the Equation x′ = Ax + f in Locally Convex Spaces

Gaston M. N’Guerekata
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Gaston M. N’Guerekata: Morgan State University

Chapter Chapter 7 in Almost Automorphic and Almost Periodic Functions in Abstract Spaces, 2001, pp 99-111 from Springer

Abstract: Abstract As an application of results obtained in Chapter 3, we will study conditions for almost periodicity of solutions of the linear differential equations x′(t) = Ax(t) + f(t), t ∈ 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 an infinitesimal generator of an equicontinuous C 0-group of linear operators.

Keywords: Linear Operator; Periodic Solution; Cauchy Sequence; Bounded Linear Operator; Convex Space (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-1-4757-4482-8_7

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