Literature cited
L. Collatz, Eigenwertaufgaben mit Technischen Anwendungen, Akademische Verlagsgesellschaft, Leipzig (1963).
S. G. Mikhlin, Variational Methods in Mathematical Physics [in Russian], Nauka, Moscow (1970).
K. O. Friedrichs, Perturbation of Spectra in Hilbert Space, Amer. Math. Soc., Providence (1965).
T. Kato, Perturbation Theory for Linear Operators, Springer, New York (1966).
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1977).
A. P. Makhmudov, “On the completeness of systems of eigenelements of some quasilinear operator equations,” Differents. Uravn.,17, No. 8, 1456–1467 (1981).
A. P. Makhmudov, Foundations of Nonlinear Spectral Analysis [in Russian], Azerb. State Univ., Baku (1984).
A. P. Makhmudov, “The completeness and the basis property of the eigenelements of nonlinear equations,” Doctoral Dissertation, Moscow (1985).
G. Fikhtengol'ts, A Course of Differential and Integral Calculus [in Russian], Vol. 1, Nauka, Moscow (1969).
S. N. Chow and J. Hale, Methods of Bifurcation Theory, Springer, New York (1982).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 3, pp. 340–347, March, 1989.
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Makhmudov, A.P., Aliev, Z.S. A nonlinear analogue of the implicit method in the theory of the perturbation of an isolated eigenvalue. Ukr Math J 41, 301–307 (1989). https://doi.org/10.1007/BF01060315
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DOI: https://doi.org/10.1007/BF01060315