Semigroups on Frechet spaces and equations with infinite delays
نویسنده
چکیده
where a∈ R,{bi}i=1 is an arbitrary sequence of real numbers, {τi} ∞ i=1 is a strictly increasing sequence of strictly positive reals such that limi→∞τi = ∞ and φ : (−∞,0] −→ R is continuous. For the special case {bi}i=1 ∈ l 1, (1.1) can be uniquely solved for any given φ ∈ BC (−∞,0], the space of all bounded real-valued continuous functions. The proof of this is indicated in Example1.2. Denote this solution by xφ . Consider the family of operators St ,t ≥ 0 on BC (−∞,0] defined as [Stφ ](θ ) = xφ (t + θ ), if t + θ > 0 = φ(t + θ ), if t + θ ≤ 0. (1.2)
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