Literature Cited
A. I. Nekrasov, Exact Theory of Steady Waves on the Surface of a Heavy Fluid [in Russian], Izd. AN SSSR, Moscow (1951).
N. N. Nazarov, “Nonlinea integral equations of Hammerstein type,” Trudy SAGU, Tashkent,5, No. 33, 79–84 (1941).
K. T. Akhmedov, “Analytical Nekrasov-Nazarov method in nonlinear analysis,” Usp. Matem. Nauk,12, No. 4, 135–153 (1957).
V. B. Melamed, “On formal solutions of some nonlinear equation,” Sib. Matem. Zh.,VI, No. 1, 165–177 (1965).
V. B. Melamed, “To questions on branched solutions of nonlinear equations,” Matem. Issled., Kishinev,IV, No. 1, (1969).
P. P. Zabreiko and B. P. Kats, “On the Nekrasov-Nazarov method of solving nonlinear equations in the case of two-dimensional degeneration,” Trudy Seminara po Funkts. Analizu, Voronezh, No. 11, 73–79 (1968).
M. Artin, “On the solution of analytic equations,” Invent. Math.,5, No. 4, 277–291 (1968).
M. A. Krasnosel'skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, and V. Ya. Stetsenko, Approximate Solutions of Operator Equations [in Russian], Nauka, Moscow (1969).
P. P. Zabreiko and M. A. Krasnosel'skii, “On bifurcation equations,” Trudy Seminara po Funkts. Analizu, Voronezh, No. 11, 80–93 (1968).
P. P. Zabreiko and M. A. Krasnosel'skii, “Simple solutions of operator equations,” Probl. Matem. Analiza Slozhnykh Sistem, Voronezh, No. 2, 31–40 (1968).
P. P. Rybin, “On the convergence of series obtained in the solution of nonlinear integral equations,” Dokl. Akad. Nauk SSSR,115, No. 3, 458–461 (1957).
V. V. Pokornyi and P. P. Rybin, “On the stabilization of the process of seeking formal implicit functions,” Usp. Matem. Nauk,XV, No. 4, 169–172 (1960).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 12, No. 5, pp. 1026–1040, September–October, 1971.
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Zabreiko, P.P., Kats, B.P. On the Nekrasov-Nazarov method of solving nonlinear operator equations. Sib Math J 12, 739–749 (1971). https://doi.org/10.1007/BF00966511
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DOI: https://doi.org/10.1007/BF00966511