Geodesic
On solvability of a Hammerstein–Voltera type nonlinear system of integral equations in critical case
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 4, pp. 71-79 
Kh. A. Khachatryan; Ts. E. Terjyan; M. F. Broyan. On solvability of a Hammerstein–Voltera type nonlinear system of integral equations in critical case. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 4, pp. 71-79. http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a7/
@article{VMJ_2016_18_4_a7,
     author = {Kh. A. Khachatryan and Ts. E. Terjyan and M. F. Broyan},
     title = {On solvability of a {Hammerstein{\textendash}Voltera} type nonlinear system of integral equations in critical case},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {71--79},
     year = {2016},
     volume = {18},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a7/}
}
TY  - JOUR
AU  - Kh. A. Khachatryan
AU  - Ts. E. Terjyan
AU  - M. F. Broyan
TI  - On solvability of a Hammerstein–Voltera type nonlinear system of integral equations in critical case
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2016
SP  - 71
EP  - 79
VL  - 18
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a7/
LA  - ru
ID  - VMJ_2016_18_4_a7
ER  - 
%0 Journal Article
%A Kh. A. Khachatryan
%A Ts. E. Terjyan
%A M. F. Broyan
%T On solvability of a Hammerstein–Voltera type nonlinear system of integral equations in critical case
%J Vladikavkazskij matematičeskij žurnal
%D 2016
%P 71-79
%V 18
%N 4
%U http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a7/
%G ru
%F VMJ_2016_18_4_a7

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

We consider Hammerstein–Voltera type nonlinear system of integral equations in critical case. Above mentioned equations have applications in rediative transfer theory and kinetic theory of gases. Using special iteration methods and method of monotone operators theory we prove the exitstence of by component positive solutions in space of bounded and summerable functions with zero limit at infinity. Some examples of corresponding equations representing separate interest are also given.

[1] Ambartsumyan V. A., Nauchnye trudy, v. 1, Izd-vo AN. ArmSSR, Erevan, 1960, 431 pp.

[2] Engibaryan N. B., “Ob odnoi zadache nelineinogo perenosa izlucheniya”, Astrofizika, 2:4 (1966), 31–36

[3] Arabadzhyan L. G., “Ob odnom integralnom uravnenii teorii perenosa v neodnorodnoi srede”, Dif. uravneniya, 23:9 (1987), 1618–1622 | Zbl

[4] Arabadzhyan L. G., Engibaryan N. B., “Uravneniya v svertkakh i nelineinye funktsionalnye uravneniya”, Itogi nauki i tekhniki. Ser. Mat. analiz, 22, 1984, 175–242

[5] Arabadzhyan L. G., “O razreshimosti odnogo integralnogo uravneniya tipa Volterra na poluosi”, Izv. NAN Armenii. Matematika, 34:2 (1999), 80–83 | Zbl

[6] Zarebina M., “A numerical Solution of Nonlinear Volterra–Fredholm Integral Equations”, J. of Appl. Analysis and Computation, 3:1 (2013), 95–104 | MR

[7] Lauran M., “Existence results for some Nonlinear Integral Equations”, Miskole Math. Notes, 13:1 (2012), 67–74 | MR | Zbl

[8] Karapetyants N. K., Kilbas A. A., Saigo M., “On the Solutions of Nonlinear Volterra Convolution Equation with power Nonlinearity”, J. of Integral Equations and Appl., 8:4 (1996), 429–445 | DOI | MR | Zbl

[9] Khachatryan Kh. A., Grigoryan S. A., “O netrivialnoi razreshimosti odnogo integralnogo uravneniya tipa Gammershteina–Volterra”, Vladikavk. mat. zhurn., 14:2 (2012), 57–66

[10] Lankaster P., Teoriya matrits, Nauka, M., 1978, 280 pp. | MR

[11] Krasnoselskii M. A., Zabreiko P. P., Pustylnik E. I., Sobolevskii P. E., Integralnye operatory v prostranstve summiruemykh funktsii, Nauka, M., 1966, 500 pp.

[12] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1981, 544 pp. | MR

[13] Khachatryan Kh. A., “Nekotorye klassy nelineinykh integralnykh uravnenii Urysona”, Dokl. BelAN. Matematika, 55:1 (2011), 5–9