Abstract
We consider a scalar linear second-order ordinary differential equation whose coefficient of the second derivative may change its sign when vanishing. For this equation, we obtain sufficient conditions for the existence of a periodic solution in the case of arbitrary periodic inhomogeneity.
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References
M. N. Eliseenko, “On periodic solutions of ordinary differential equations of the second order unsolvable with respect to derivative,” Differents. Uravn., 21, No. 9, 1618–1621 (1985).
V. A. Eremenko, Periodic Solutions of Degenerate Linear Systems of Ordinary Differential Equations of the Second Order [in Russian], Dep. at UkrNIINTI, No. 2800-Uk, Ternopol (1986).
A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Oscillations. Invariant Tori [in Russian], Nauka, Moscow (1987).
Yu. Mozer, “Rapidly convergent iterative method and nonlinear differential equations,” Usp. Mat. Nauk, 23, No. 4, 179–238 (1986).
Additional information
Ternopol Academy of National Economy, Ternopol. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 8, pp. 1137–1142, August, 1997.
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Eremenko, V.A. On periodic solutions of linear degenerate second-order ordinary differential equations. Ukr Math J 49, 1279–1285 (1997). https://doi.org/10.1007/BF02487553
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DOI: https://doi.org/10.1007/BF02487553