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\(AP_{r}\)-almost periodic solutions to the equation \(\dot{x}(t)= ax(t)+(k\ast x)(t)+f(t)\). (English) Zbl 1244.34094

Summary: This note is dedicated to the existence of almost periodic solutions of a certain class of functional equations, of the form (1) in the text, in spaces like \(AP_r(R, {\mathcal C}^n), 1\leq r\leq 2\). Frequency domain conditions are involved in this study.

MSC:

34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
34K05 General theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
34K40 Neutral functional-differential equations
34K06 Linear functional-differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
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Full Text: Euclid

References:

[1] C. Corduneanu, A scale of almost periodic function spaces. Differential and Integral Equations 24 , Numbers 1-2 (2011), 1-27. · Zbl 1240.42115
[2] C. Corduneanu, M. Mahdavi, and Y. Li, Special Topics in The Theory of Functional Equations , (Ch.4) (in preparation).
[3] C. L. DeVito, Harmonic Analysis , Jones and Bartlett Publishers Inc., Boston 2007.
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