The solvability of Volterra integro-differential equations with Fredholm operator in main part
The Bulletin of Irkutsk State University. Series Mathematics, Tome 5 (2012) no. 3, pp. 73-93

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

An initial value problem unique solvability in the classes of distributions and functions of finite smoothness is studied in this paper by the methods of the theory of fundamental operator-functions of integro-differential operators in Banach spaces.
Keywords: Banach space, Fredholm operator, fundamental operator-function.
Mots-clés : Jordan set, distribution
S. S. Orlov. The solvability of Volterra integro-differential equations with Fredholm operator in main part. The Bulletin of Irkutsk State University. Series Mathematics, Tome 5 (2012) no. 3, pp. 73-93. http://geodesic.mathdoc.fr/item/IIGUM_2012_5_3_a6/
@article{IIGUM_2012_5_3_a6,
     author = {S. S. Orlov},
     title = {The solvability of {Volterra} integro-differential equations with {Fredholm} operator in main part},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {73--93},
     year = {2012},
     volume = {5},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2012_5_3_a6/}
}
TY  - JOUR
AU  - S. S. Orlov
TI  - The solvability of Volterra integro-differential equations with Fredholm operator in main part
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2012
SP  - 73
EP  - 93
VL  - 5
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2012_5_3_a6/
LA  - ru
ID  - IIGUM_2012_5_3_a6
ER  - 
%0 Journal Article
%A S. S. Orlov
%T The solvability of Volterra integro-differential equations with Fredholm operator in main part
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2012
%P 73-93
%V 5
%N 3
%U http://geodesic.mathdoc.fr/item/IIGUM_2012_5_3_a6/
%G ru
%F IIGUM_2012_5_3_a6

[1] M. M. Vainberg, V. A. Trenogin, Teoriya vetvleniya reshenii nelineinykh integralnykh uravnenii, Nauka, M., 1969, 527 pp. | MR

[2] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979, 320 pp. | MR

[3] A. A. Ilyushin, B. E. Pobedrya, Osnovy matematicheskoi teorii vyazkouprugosti, Nauka, M., 1970, 280 pp. | MR

[4] B. V. Loginov, Yu. B. Rusak, “Obobschennaya zhordanova struktura v teorii vetvleniya”, Pryamye i obratnye zadachi dlya differentsialnykh uravnenii v chastnykh proizvodnykh i ikh prilozheniya, FAN, Tashkent, 1978, 133–148 | MR

[5] S. S. Orlov, “Vyrozhdennoe integro-differentsialnoe uravnenie v banakhovykh prostranstvakh i ego prilozheniya”, Izv. Irkut. gos. un-ta. Ser. Matematika, 3:1 (2010), 54–60 | Zbl

[6] A. P. Oskolkov, “Nachalno-kraevye zadachi dlya uravnenii dvizhenii zhidkostei Kelvina–Foigta i Oldroita”, Tr. MIAN SSSR, 179, 1988, 126–164 | MR

[7] N. A. Sidorov, “Ob odnom klasse uravnenii Volterra s vyrozhdeniem v banakhovykh prostranstvakh”, Sib. mat. zhurn., 21:2 (1983), 202–203

[8] N. A. Sidorov, D. N. Sidorov, “Posledovatelnye priblizheniya reshenii vyrozhdennoi zadachi Koshi”, Tr. In-ta matematiki i mekhaniki UrO RAN, 18, no. 2, 2012, 238–244

[9] N. A. Sidorov, D. N. Sidorov, A. V. Krasnik, “O reshenii operatorno-integralnykh uravnenii Volterra v neregulyarnom sluchae metodom posledovatelnykh priblizhenii”, Differentsialnye uravneniya, 46:6 (2010), 874–878 | MR

[10] M. V. Falaleev, “O prilozheniyakh teorii fundamentalnykh operator-funktsii vyrozhdennykh integro-differentsialnykh operatorov v banakhovykh prostranstvakh”, Neklassicheskie uravneniya matematicheskoi fiziki, Izd-vo IM im. S. L. Soboleva SO RAN, Novosibirsk, 283–297

[11] M. V. Falaleev, S. S. Orlov, “Vyrozhdennye integro-differentsialnye uravneniya spetsialnogo vida v banakhovykh prostranstvakh i ikh prilozheniya”, Vestn. YuUrGU. Matematicheskoe modelirovanie i programmirovanie, 2011, no. 4, Vyp. 7, 100–110 | Zbl

[12] M. V. Falaleev, S. S. Orlov, “Nachalno-kraevye zadachi dlya integro-differentsialnykh uravnenii vyazkouprugosti”, Obozrenie prikladnoi i promyshlennoi matematiki, 17:4 (2010), 597–600 | MR

[13] M. V. Falaleev, “Integro-differentsialnye uravneniya s fredgolmovym operatorom pri starshei proizvodnoi v banakhovykh prostranstvakh i ikh prilozheniya”, Izv. Irkut. gos. un-ta. Ser. Matematika, 5:2 (2012), 90–102 | Zbl

[14] M. M. Cavalcanti, V. N. Domingos Cavalcanti, J. Ferreira, “Existence and Uniform Decay for a Non-Linear Viscoelastic Equation with Strong Damping”, Math. Meth. Appl. Sci., 24 (2001), 1043–1053 | DOI | MR | Zbl

[15] N. Sidorov, B. Loginov, A. Sinithyn, M. Falaleev, Lyapunov–Schmidt methods in nonlinear analysis and applications, Kluwer Acad. Publ., Dordrecht, 2002, 548 pp. | MR | Zbl