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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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