Geodesic
Delay differential equations with differentiable solution operators on open domains in $C((-\infty,0],\mathbb{R}^n)$ and processes for Volterra integro-differential equations
Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 483-506.

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For autonomous delay differential equations $x'(t)=f(x_t)$ we construct a continuous semiflow of continuously differentiable solution operators $x_0\mapsto x_t$, $t\ge0$, on open subsets of the Fréchet space $C((-\infty,0],\mathbb{R}^n)$. 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 $x'(t)=\int_0^tk(t,s)h(x(s))ds$. 
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H.-O. Walther. Delay differential equations with differentiable solution operators on open domains in $C((-\infty,0],\mathbb{R}^n)$ and processes for Volterra integro-differential equations. Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 483-506. http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a5/

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