Geodesic
Evolution systems for differential equations with variable time lags
Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 4, Tome 48 (2013), pp. 5-26

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We consider nonautonomous retarded functional differential equations under hypotheses which are designed for the application to equations with variable time lags, which may be unbounded, and construct an evolution system of solution operators which are continuously differentiable. These operators are defined on manifolds of continuously differentiable functions. The results apply to pantograph equations and to nonlinear Volterra integro-differential equations, for example. For linear equations we also provide a simpler evolution system with solution operators on a Banach space of continuous functions. 
@article{CMFD_2013_48_a0,
     author = {H.-O. Walther},
     title = {Evolution systems for differential equations with variable time lags},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {5--26},
     publisher = {mathdoc},
     volume = {48},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2013_48_a0/}
}
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H.-O. Walther. Evolution systems for differential equations with variable time lags. Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 4, Tome 48 (2013), pp. 5-26. http://geodesic.mathdoc.fr/item/CMFD_2013_48_a0/