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. 
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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/

[1] Kheil Dzh., Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984

[2] Davidenko D. F., “Ob odnom novom metode chislennogo resheniya sistem nelineinykh uravnenii”, Dokl. AN SSSR, 88:4 (1953), 601–602 | MR | Zbl

[3] Grigolyuk E. I., Shalashilin V. I., Problemy nelineinogo deformirovaniya, Nauka, M., 1988 | Zbl

[4] Shalashilin V. I., Kuznetsov E. B., “Nailuchshii parametr prodolzheniya resheniya”, Dokl. RAN, 334:5 (1994), 566–568 | MR | Zbl

[5] Kuznetsov E. B., Shalashilin V. I., “Zadacha Koshi kak zadacha prodolzheniya po nailuchshemu parametru”, Differents. uravneniya, 30:6 (1994), 964–971 | MR | Zbl

[6] Ortega Dzh., Pul U., Vvedenie v chislennye metody resheniya differentsialnykh uravnenii, Nauka, M., 1986 | Zbl

[7] Shalashilin V. I., Kuznetsov E. B., “Zadacha Koshi dlya nelineino deformiruemykh sistem kak zadacha prodolzheniya resheniya po parametru”, Dokl. RAN, 329:4 (1993), 426–428 | MR | Zbl

[8] Kuznetsov E. B., Shalashilin V. I., “Zadacha Koshi kak zadacha prodolzheniya resheniya po parametru”, ZhVMiMF, 33:12 (1993), 1792–1805 | MR | Zbl

[9] Kuznetsov E. B., Shalashilin V. I., “Zadacha Koshi dlya mekhanicheskikh sistem s konechnym chislom stepenei svobody kak zadacha prodolzheniya po nailuchshemu parametru”, PMM, 58:6 (1994), 14–21 | MR