Abstract
We study the problem of the existence of periodic solutions of two-dimensional linear inhomogeneous periodic systems of differential equations for which the corresponding homogeneous system is Hamiltonian. We propose a new numerical-analytic algorithm for the investigation of the problem of the existence of periodic solutions of two-dimensional nonlinear differential systems with Hamiltonian linear part and their construction. The results obtained are generalized to systems of higher orders.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 4, pp. 483–495, April, 2005.
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Korol', I.I. On Periodic Solutions of One Class of Systems of Differential Equations. Ukr Math J 57, 583–599 (2005). https://doi.org/10.1007/s11253-005-0212-9
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DOI: https://doi.org/10.1007/s11253-005-0212-9