We substantiate the applicability of the approximation-iterative method to weakly nonlinear integral equations with restrictions.
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A. Yu. Luchka and V. F. Mel’nychuk, “Iterative method for quasilinear integral equations with constraints,” Nelin. Kolyvannya, 14, No. 4, 496–506 (2011); English translation: Nonlin. Oscillations, 14, No. 4, 526–536 (2012).
A. Yu. Luchka, “General approach to the construction of methods of approximation-iterative type,” Visn. Derzh. Univ. “L’vivs’ka Politekhnika,” No. 3, 212–216 (2000).
A. Yu. Luchka, “Integral equations with restrictions and methods for their solution,” Kibern. Sist. Analiz, No. 3, 82–96 (19960.
A. Yu. Luchka, “Methods for the solution of equations with restrictions and the Sokolov projection-iterative method,” Ukr. Mat. Zh., 48, No. 11, 1501–1509 (1996); English translation: Ukr. Math. J., 48, No. 11, 1696–1707 (1996).
A. Yu. Luchka, “Methods for the investigation of systems of differential equations with restrictions,” in: Proceedings of the Ukrainian Mathematical Congress “Differential Equations and Nonlinear Oscillations” (Kyiv, 2002) [in Ukrainian] (2002), pp. 43–59.
A. Yu. Luchka and O. B. Nesterenko, “Methods for the solution of boundary-value problems for weakly nonlinear integro-differential equations with parameters and restrictions,” Ukr. Mat. Zh., 61, No. 5, 672–679 (2009); English translation: Ukr. Math. J., 61, No. 5, 801–809 (2009).
A. Yu. Luchka and V. A. Feruk, “Construction of approximate solutions of systems of differential equations with parameters and restrictions,” Nelin. Kolyvannya, 13, No. 3, 361–378 (2010); English translation: Nonlin. Oscillations, 13, No. 3, 389–406 (2010).
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Translated from Neliniini Kolyvannya, Vol. 15, No. 1, pp. 89–111, January–March, 2012.
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Luchka, A.Y., Mel’nychuk, V.F. Approximation-iterative method for weakly nonlinear integral equations with restrictions. J Math Sci 187, 471–493 (2012). https://doi.org/10.1007/s10958-012-1077-8
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DOI: https://doi.org/10.1007/s10958-012-1077-8