Article

    Ufa Mathematical Journal
    Volume 3, Number 2, pp. 19-26

    On necessary conditions for existence of periodic solutions in a dynamic system with discontinuous nonlinearity and an external periodic influence.


    Yevstafyeva V.V.

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    In Euclidean space the system of ordinary differential equations with discontinuous nonlinearity of non-ideal relay type and external continuous periodic influence in the right part is considered. Necessary conditions for the coefficients of the system for the existence of periodic solutions with given properties in the problems of the specified class are obtained by accurate analytical methods. The approach for finding the moments of time and the switching points of the image point of the required solution is offered in the case when the period of the solution is multiple to the period of the function, describing the external perturbation.