Geodesic
Continuous branches of multivalued mappings and functional-differential inclusions with nonconvex right-hand side
Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 273-287 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is proved that in the space of Bochner-integrable mappings a multivalued mapping with nonconvex images has a continuous branch that, for a given single-valued mapping and for a previously specified accuracy, realizes the distance between the images of the single-valued mapping and the multivalued mapping. This result is applied to the investigation of properties of solutions of functional-differential inclusions with nonconvex right-hand side. 
@article{SM_1992_71_2_a0,
     author = {A. I. Bulgakov},
     title = {Continuous branches of multivalued mappings and functional-differential inclusions with nonconvex right-hand side},
     journal = {Sbornik. Mathematics},
     pages = {273--287},
     year = {1992},
     volume = {71},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1992_71_2_a0/}
}
TY  - JOUR
AU  - A. I. Bulgakov
TI  - Continuous branches of multivalued mappings and functional-differential inclusions with nonconvex right-hand side
JO  - Sbornik. Mathematics
PY  - 1992
SP  - 273
EP  - 287
VL  - 71
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1992_71_2_a0/
LA  - en
ID  - SM_1992_71_2_a0
ER  - 
%0 Journal Article
%A A. I. Bulgakov
%T Continuous branches of multivalued mappings and functional-differential inclusions with nonconvex right-hand side
%J Sbornik. Mathematics
%D 1992
%P 273-287
%V 71
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1992_71_2_a0/
%G en
%F SM_1992_71_2_a0
A. I. Bulgakov. Continuous branches of multivalued mappings and functional-differential inclusions with nonconvex right-hand side. Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 273-287. http://geodesic.mathdoc.fr/item/SM_1992_71_2_a0/

[1] Blagodatskikh V. I., “Nekotorye rezultaty po teorii differentsialnykh vklyuchenii”, Summer School on Ordinary Differential Equations, 2, Brno, 1974, 29–67

[2] Azbelev N. V., Maksimov V. P., “Uravneniya s zapazdyvayuschim argumentom”, Differents. uravneniya, 18:12 (1982), 2027–2050 | MR | Zbl

[3] Antosiewicz H. A., Cellina A., “Continuous selections and differential relations”, J. Differ. Equations, 19:2 (1975), 386–399 | DOI | MR

[4] Fryskowski A., “Continuous selections for a class of non-convex multivalued maps”, Studia Math. (PRL), 76:2 (1983), 163–174 | MR

[5] Ioffe A. D., Tikhomirov V. M., Teoriya ekstremalnykh zadach, Nauka, M., 1974 | MR | Zbl

[6] Cellina A., Colombo G., Fonda A., “Approximate selections and fixed points for upper semicontinuous maps with decomposable values”, Pros. Amer. Math. Soc., 98:4 (1986), 663–666 | DOI | MR | Zbl

[7] Bogatyrev A. V., “Nepreryvnye vetvi mnogoznachnykh otobrazhenii s nevypukloi pravoi chastyu”, Matem. sb., 120(162) (1983), 344–353 | MR

[8] Bulgakov A. I., “K voprosu suschestvovaniya nepreryvnykh vetvei mnogoznachnykh otobrazhenii s nevypuklymi obrazami v prostranstvakh summiruemykh funktsii”, Matem. sb., 136(178) (1988), 292–299

[9] Bulgakov A. I., “Nepreryvnye vetvi mnogoznachnykh otobrazhenii s nevypuklymi obrazami i funktsionalno-differentsialnye vklyucheniya”, Differents. uravneniya, 22:10 (1986), 1659–1670 | MR | Zbl

[10] Pianigiani G., “On the fundamential theory of multivalued differential equations”, J. Differ. Equation, 25:1 (1977), 30–38 | DOI | MR | Zbl

[11] Tolstonogov A. A., Chugunov P. I., “O mnozhestve reshenii differentsialnogo vklyucheniya v banakhovom prostranstve”, Sib. matem. zhurn., 24:6 (1983), 144–159 | MR | Zbl

[12] Chugunov P. I., “Svoistva reshenii differentsialnykh vklyuchenii i upravlyaemye sistemy”, Prikladnaya matematika i pakety prikladnykh programm, SEI SO AN SSSR, Irkutsk, 1980, 155–179

[13] Bulgakov A. I., “Funktsionalno-differentsialnoe vklyuchenie s operatorom, imeyuschim nevypuklye obrazy”, Differents. uravneniya, 23:10 (1987), 1659–1668 | MR | Zbl

[14] Krasnoselskii M. A., Zabreiko P. P., Pustylnik E. I., Sobolevskii P. E., Integralnye operatory v prostranstvakh summiruemykh funktsii, Nauka, M., 1966 | MR

[15] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977 | MR | Zbl

[16] Tikhonov A. N., “O funktsionalnykh uravneniyakh tipa Volterra i ikh prilozheniyakh k nekotorym zadacham matematicheskoi fiziki”, Byulleten MGU, sekts. A, matem. i mekhan., 1:8 (1938), 1–25 | MR | Zbl

[17] Bulgakov A. I., Maksimov V. P., “Funktsionalnye i funktsionalno-differentsialnye vklyucheniya s volterrovymi operatorami”, Differents. uravneniya, 17:8 (1981), 1362–1374 | MR | Zbl

[18] Azbelev N. V., Tsalyuk Z. B., “Ob integralnykh neravenstvakh”, Matem. sb., 56(98) (1962), 325–342 | MR

[19] Barbashin E. A., Alimov Yu. I., “K teorii releinykh differentsialnykh uravnenii”, Izv. Vuzov. Matem., 1962, no. 1(26), 3–13 | Zbl

[20] Davy J. L., “Properties of the solution set of generalised differential equation”, Bull. Austral. Math. Soc., 6:3 (1972), 379–398 | DOI | MR | Zbl

[21] Bulgakov A. I., Lyapin L. N., “Ob integralnom vklyuchenii s funktsionalnym operatorom”, Differents. uravneniya, 15:5 (1979), 876–884 | MR

[22] Filippov A. F., “Klassicheskie resheniya differentsialnykh uravnenii s mnogoznachnoi pravoi chastyu”, Vestn. MGU. Ser. 1. Matem., mekh., 1967, no. 3, 16–26 | Zbl

[23] Filippov A. F., “O suschestvovanii reshenii mnogoznachnykh differentsialnykh uravnenii”, Matem. zametki, 10:3 (1971), 307–313 | MR | Zbl