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Periodic solutions of nonlinear second-order equations which are not solved for the highest derivative

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Literature cited

  1. A. M. Samoilenko, “Periodic solutions of nonlinear second-order equations,” Differentsial', Urav.,3, No. 11 (1967).

  2. A. M. Samoilenko, “Numeric-analytic method of investigating periodic systems of ordinary differential equations. I,” Ukr. Matem. Zh.,17, No. 4 (1965).

  3. A. M. Samoilenko, “Numeric-analytic method of investigating periodic systems of ordinary differential equations. II,” Ukr. Matem. Zh.,18, No. 2 (1966).

  4. A. P. Torzhevskii, “Periodic solutions of the equation of planar oscillations of a satellite in an elliptic orbit,” Kosmich. Issled.,2, No. 5 (1964).

  5. N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Ed. 3, Fizmatgiz, Moscow (1963).

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Authors and Affiliations

  1. Kiev State University, USSR

    Yu. D. Shlapak

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  1. Yu. D. Shlapak
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 26, No. 6, pp. 850–854, November–December, 1974.

The author thanks A. M. Samoilenko for posing this problem and for his constant attention to this work.

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Shlapak, Y.D. Periodic solutions of nonlinear second-order equations which are not solved for the highest derivative. Ukr Math J 26, 702–706 (1974). https://doi.org/10.1007/BF01085271

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  • DOI: https://doi.org/10.1007/BF01085271

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