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On the initial value problem for functional differential systems. (English) Zbl 0801.34062
Under suitable (and rather natural) assumptions, the authors prove that the problem $$x^{(n)}(t)= f(t,x_ t,\dots, x_ t^{(n-1)})$$ $$(b\leq t<+\infty)$$, $$x^{(k)}= \psi^{(k)}$$ $$(k= 0,\dots,n- 1)$$ admits a solution and the solution set is a compact $$R_ \delta$$ set in the Fréchet space $$C^{n-1}([b- h,+\infty),R^ n)$$ whose topology is determinated by seminorms $$p_ m(x)= \sup\Bigl\{\sum^{n-1}_{k=0} | x^{(k)}(t)|: b- h\leq t\leq b+m\Bigr\}$$.

##### MSC:
 34K05 General theory of functional-differential equations 34K25 Asymptotic theory of functional-differential equations
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