Geodesic
Transformation of equations with retarded argument to equations with the best argument
Matematičeskie zametki, Tome 63 (1998) no. 1, pp. 62-68

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The problem of choosing the best argument in the Cauchy problem for a system of ordinary differential equations with retarded argument is studied from the viewpoint of the method of continuation of the solution with respect to a parameter. It is proved that the arc length counted along the integral curve of the problem is the best argument for the system of continuation equations to be well-posed in the best possible way. A transformation of the Cauchy problem to the best argument is obtained. 
@article{MZM_1998_63_1_a6,
     author = {E. B. Kuznetsov},
     title = {Transformation of equations with retarded argument to equations with the best argument},
     journal = {Matemati\v{c}eskie zametki},
     pages = {62--68},
     publisher = {mathdoc},
     volume = {63},
     number = {1},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_1_a6/}
}
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E. B. Kuznetsov. Transformation of equations with retarded argument to equations with the best argument. Matematičeskie zametki, Tome 63 (1998) no. 1, pp. 62-68. http://geodesic.mathdoc.fr/item/MZM_1998_63_1_a6/