Geodesic
On the differentiability with respect to the initial condition of a solution to an ordinary differential equation
Sbornik. Mathematics, Tome 35 (1979) no. 1, pp. 115-129 
M. F. Sukhinin. On the differentiability with respect to the initial condition of a solution to an ordinary differential equation. Sbornik. Mathematics, Tome 35 (1979) no. 1, pp. 115-129. http://geodesic.mathdoc.fr/item/SM_1979_35_1_a7/
@article{SM_1979_35_1_a7,
     author = {M. F. Sukhinin},
     title = {On the differentiability with respect to the initial condition of a~solution to an ordinary differential equation},
     journal = {Sbornik. Mathematics},
     pages = {115--129},
     year = {1979},
     volume = {35},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1979_35_1_a7/}
}
TY  - JOUR
AU  - M. F. Sukhinin
TI  - On the differentiability with respect to the initial condition of a solution to an ordinary differential equation
JO  - Sbornik. Mathematics
PY  - 1979
SP  - 115
EP  - 129
VL  - 35
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1979_35_1_a7/
LA  - en
ID  - SM_1979_35_1_a7
ER  - 
%0 Journal Article
%A M. F. Sukhinin
%T On the differentiability with respect to the initial condition of a solution to an ordinary differential equation
%J Sbornik. Mathematics
%D 1979
%P 115-129
%V 35
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1979_35_1_a7/
%G en
%F SM_1979_35_1_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

In this article a version of the theorem on differentiability of an implicit function is proved, and is then applied to establish a theorem on the differentiability with respect to the initial condition of a solution to an ordinary differential equation in a locally convex space obtained by introducing into a Banach space a locally convex topology satisfying certain conditions. An example is exhibited which cannot be studied by previously known theorems of this type. Bibliography: 13 titles.

[1] A. Kartan, Differentsialnoe ischislenie. Differentsialnye formy, izd-vo “Mir”, Moskva, 1971 | MR

[2] N. Papaghiuc, “Un théorème d'existence pour les équations différentielles ordinaires dans les espaces locallement convexes”, An. Sti. Univ. Iasi, XXI:1a (1975), 85–94 | MR

[3] V. I. Averbukh, O. G. Smolyanov, “Razlichnye opredeleniya proizvodnoi v lineinykh topologicheskikh prostranstvakh”, Uspekhi matem. nauk, XXIII:4(142) (1968), 67–116

[4] M. F. Sukhinin, “Neskolko teorem ob obratnoi i neyavnoi funktsiyakh v lineinykh topologicheskikh prostranstvakh”, Uspekhi matem. nauk, XXVIII:1(169) (1973), 251–252

[5] M. F. Sukhinin, Teorema o neyavnoi funktsii v lineinykh topologicheskikh prostranstvakh, Dissertatsiya, MGU, 1972

[6] R. Edvards, Funktsionalnyi analiz, izd-vo “Mir”, Moskva, 1969

[7] V. I. Averbukh, O. G. Smolyanov, “Teoriya differentsirovaniya v lineinykh topologicheskikh prostranstvakh”, Uspekhi matem. nauk, XXII:6(138) (1967), 201–260

[8] M. A. Krasnoselskii, P. P. Zabreiko, E. I. Pustylnik, P. E. Sobolevskii, Integralnye operatory v prostranstvakh summiruemykh funktsii, izd-vo “Nauka”, Moskva, 1966 | MR

[9] I. I. Gikhman, A. V. Skorokhod, Teoriya sluchainykh protsessov, t. 3, izd-vo “Nauka”, Moskva, 1975 | MR | Zbl

[10] B. Stankovich, “Diferentsijalne jednachine u lokalno konveksnim prostorima”, Matem. vesnik, 7(22):4 (1970), 551–558 | Zbl

[11] A. N. Godunov, Nekotorye svoistva differentsialnykh uravnenii v lokalno vypuklykh prostranstvakh, Dissertatsiya, MGU, 1973

[12] S. Kato, “On existence and uniqueness conditions for nonlinear ordinary differential equations in Banach spaces”, Funkc. ekvacioj, 19:3 (1976), 239–245 | MR | Zbl

[13] Ya. V. Radyno, “Lineinye differentsialnye uravneniya v lokalno vypuklykh prostranstvakh. I. Regulyarnye operatory i ikh svoistva”, Diff. uravneniya, 13:8 (1977), 1402–1410 | MR | Zbl