Literature cited
M. M. Vainberg, Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations, Halsted Press (1974).
A. I. Perov, “On potential operators,” Mat. Zametki,24, No. 6, 793–799 (1978).
A. I. Perov and V. L. Khatskevich, “On some local existence theorems for periodic solutions,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 7, 50–60 (1982).
R. T. Rockafellar, “Monotone operators associated with saddle-functions and minimax problems,” in: Nonlinear Functional Analysis, Proc. Symp. Pure Math., Vol. 18, Part 1, Amer. Math. Soc., Providence (1970), pp. 241–250.
A. I. Perov, Variational Methods of the Theory of Nonlinear Oscillations [in Russian], Voronezh State Univ. (1981).
I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland, Amsterdam (1976).
M. A. Krasnosel'skii and A. I. Perov, “On the existence of solutions of certain non-linear operator equations,” Dokl. Akad. Nauk SSSR,126, No. 1, 15–18 (1959).
M. A. Krasnosel'skii and P. P. Zabreiko, Geometric Methods of Nonlinear Analysis [in Russian], Nauka, Moscow (1975).
F. E. Browder, Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces, Proc. Symp. Pure Math., Vol. 18, Part 2, Am. Math. Soc., Providence (1976).
R. I. Kachurovskii, “Nonlinear monotone operators in Banach spaces,” Usp. Mat. Nauk,23, No. 2, 121–168 (1968).
A. I. Perov and Yu. V. Trubnikov, “Monotone differential equations,” Differents. Uravn.,12, No. 7, 1223–1237 (1976).
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Translated from Matematicheskie Zametki, Vol. 36, No. 3, pp. 377–387, September, 1984.
In conclusion, the author expresses gratitude to A. I. Perov.
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Khatskevich, V.L. Potential operators. Mathematical Notes of the Academy of Sciences of the USSR 36, 687–692 (1984). https://doi.org/10.1007/BF01141941
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DOI: https://doi.org/10.1007/BF01141941