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$AP_r$-Almost Periodic Solutions to the Equations $x'(t) = Ax(t) + (k \ast x)(t) + f(t)$

Volume 12, Number 2 (2011), 43 - 47

$AP_r$-Almost Periodic Solutions to the Equations $x'(t) = Ax(t) + (k \ast x)(t) + f(t)$

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Abstract

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 $AP_r({\mathbb R}, {\cal C}^n)$, $1\leq r\leq 2$. Frequency domain conditions are involved in this study.