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 
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/
@article{CMFD_2021_67_3_a5,
     author = {H.-O. Walther},
     title = {Delay differential equations with differentiable solution operators on open domains in $C((-\infty,0],\mathbb{R}^n)$ and processes for {Volterra} integro-differential equations},
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     pages = {483--506},
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     volume = {67},
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     url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a5/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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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