Geodesic
The continuous dependence of solutions to Volterra equations with locally contracting operators on parameters
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 16-29

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For a Volterra equation in a functional space we obtain conditions for the unique existence of a global or maximally extended solution and its continuous dependence on equation parameters. Based on these results, we state conditions for the solvability of the Cauchy problem for a differential equation with delay and the continuous dependence of solutions on the right-hand side of the equation, on the delay, on the initial condition, and the history.
Keywords: Volterra operators, continuous dependence of solutions to equations on parameters, locally contracting operators, differential equations with delay. 
@article{IVM_2010_8_a1,
     author = {E. O. Burlakov and E. S. Zhukovskii},
     title = {The continuous dependence of solutions to {Volterra} equations with locally contracting operators on parameters},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {16--29},
     publisher = {mathdoc},
     number = {8},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_8_a1/}
}
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E. O. Burlakov; E. S. Zhukovskii. The continuous dependence of solutions to Volterra equations with locally contracting operators on parameters. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 16-29. http://geodesic.mathdoc.fr/item/IVM_2010_8_a1/