Delay differential equations with differentiable solution operators on open domains in $C((-\infty,0],\mathbb{R}^n)$, and processes for Volterra integro-differential equations
Abstract:For autonomous delay differential equations x ′ (t) = f (xt) we construct a continuous semiflow of continuously differentiable solution operators x 0 → xt, t ≥ 0, on open subsets of the Fréchet space C((−∞, 0], R n ). For nonautonomous equations this yields a continuous process of differentiable solution operators. As an application we obtain processes which incorporate all solutions of Volterra integro-differential equations x ′ (t) = t 0 k(t, s)h(x(s))ds.
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