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On Periodic Solutions of Autonomous Systems

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We propose a method for the investigation of periodic solutions of autonomous dynamical systems described by ordinary differential equations with phase and integral restrictions. We formulate the general problem of periodic solutions as a boundary-value problem with restrictions. By introducing a fictitious control, we transform the boundary-value problem into a control problem for dynamical systems with phase and integral restrictions. The control problem is solved by reducing it to an integral Fredholm equation of the first kind. We establish necessary and sufficient conditions for the existence of periodic solutions and propose an algorithm for finding periodic solution according to the limit points of the minimizing sequences.

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  1. Al-Farabi Kazakh National University, Al-Farabi Avenue 71, Building 13, Almaty, Kazakhstan, 050040

    S. A. Aisagaliev

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  1. S. A. Aisagaliev
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Correspondence to S. A. Aisagaliev.

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Translated from Neliniini Kolyvannya, Vol. 20, No. 1, pp. 3–19, January–March, 2017.

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Aisagaliev, S.A. On Periodic Solutions of Autonomous Systems. J Math Sci 229, 335–353 (2018). https://doi.org/10.1007/s10958-018-3681-8

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  • DOI: https://doi.org/10.1007/s10958-018-3681-8

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