Almost periodic solutions of nonlinear hyperbolic equations with time delay.

Poorkarimi, Hushang; Wiener, Joseph

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We present a method for constructing almost periodic sequences and functions with values in a metric space. Applying this method, we find almost periodic sequences and functions with prescribed values. Especially, for any totally bounded countable set $X$ in a metric space, it is proved the existence of an almost periodic sequence ${ψ_{k}}_{k \in ℤ}$ such that ${ψ_{k}; k \in ℤ} = X$ and $ψ_{k} = ψ_{k + l q (k)}$ , $l \in ℤ$ for all $k$ and some $q (k) \in ℕ$ which depends on $k$ .