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.

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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. 
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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