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

Voir la notice de l'article 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 $x'(t)=\int_0^tk(t,s)h(x(s))ds$. 
@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},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {483--506},
     publisher = {mathdoc},
     volume = {67},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a5/}
}
TY  - JOUR
AU  - H.-O. Walther
TI  - Delay differential equations with differentiable solution operators on open domains in $C((-\infty,0],\mathbb{R}^n)$ and processes for Volterra integro-differential equations
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2021
SP  - 483
EP  - 506
VL  - 67
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a5/
LA  - ru
ID  - CMFD_2021_67_3_a5
ER  - 
%0 Journal Article
%A H.-O. Walther
%T Delay differential equations with differentiable solution operators on open domains in $C((-\infty,0],\mathbb{R}^n)$ and processes for Volterra integro-differential equations
%J Contemporary Mathematics. Fundamental Directions
%D 2021
%P 483-506
%V 67
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a5/
%G ru
%F CMFD_2021_67_3_a5
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/