Geodesic
On one Urysohn type nonlinear integral equation with noncompact operator
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2010), pp. 23-28 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the present paper the Urysohn type nonlinear integral equation with noncompact operator on the half-line is considered. It is assumed that the Wiener-Hopf-Hankel type operator is a local minorant for the initial Urysohn operator. The existence of a positive and bounded solution is proved. The limit of constructed solution at infinity is calculated. At the end of the work a list of examples is given.
Keywords: nonlinearity, iterative methods, Urysohn operator, Caratheodory condition. 
@article{UZERU_2010_3_a1,
     author = {Kh. A. Khachatryan},
     title = {On one {Urysohn} type nonlinear integral equation with noncompact operator},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {23--28},
     year = {2010},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2010_3_a1/}
}
TY  - JOUR
AU  - Kh. A. Khachatryan
TI  - On one Urysohn type nonlinear integral equation with noncompact operator
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2010
SP  - 23
EP  - 28
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/UZERU_2010_3_a1/
LA  - en
ID  - UZERU_2010_3_a1
ER  - 
%0 Journal Article
%A Kh. A. Khachatryan
%T On one Urysohn type nonlinear integral equation with noncompact operator
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2010
%P 23-28
%N 3
%U http://geodesic.mathdoc.fr/item/UZERU_2010_3_a1/
%G en
%F UZERU_2010_3_a1
Kh. A. Khachatryan. On one Urysohn type nonlinear integral equation with noncompact operator. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2010), pp. 23-28. http://geodesic.mathdoc.fr/item/UZERU_2010_3_a1/

[1] A. Kufner, S. Fuchik, Nonlinear Differential Equations, Nauka, M., 1988, 304 pp. | MR | Zbl

[2] Kh.A. Khachatryan, “Sufficient conditions for the solvability of the Uryson integral equation on a half-axis”, Doklady RAN. Matematica, 425:2 (2009), 462–465 (in Russian) | MR | Zbl

[3] B. N. Yengibaryan, “Application of Multiple Factorization to Convolution-Type Homogeneous Equations”, Izv. NAN Armenii, Matematica, 32:1 (1997), 38–48 (in Russian) | MR

[4] A.N. Kolmogorov, V.S. Fomin, Elements of the Theory of Functions and Functional Analysis, Nauka, M., 1981, 544 pp. | MR | Zbl

[5] L. G. Arabadzhyan, “On an integral equation of transport theory in an inhomogeneous medium”, Differ. Uravn., 23:9 (1987), 1618–1622 | MR | Zbl