Almost Periodic Solutions of the Equation x′ = Ax + f in Locally Convex Spaces
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.
KeywordsLinear Operator Periodic Solution Cauchy Sequence Bounded Linear Operator Convex Space
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- K. Yosida, Functional Analysis, Springer-Verlag, 1968.Google Scholar