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Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series

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On strongly irregular periodic solutions of the linear nonhomogeneous discrete equation of the first order

https://doi.org/10.29235/1561-2430-2020-56-1-30-35

Abstract

As is proved earlier (the Massera theorem), the first-order scalar periodic ordinary differential equation does not have strongly irregular periodic solutions (solutions with a period incommensurable with the period of the equation). For difference equations with discrete time, strong irregularity means that the equation period and the period of its solution are relatively prime numbers. It is known that in the case of discrete equations, the mentioned result has no complete analog.

The purpose of this paper is to investigate the possibility of realizing an analog of the Massera theorem for certain classes of difference equations. To do this, we consider the class of linear difference equations. It is proved that a linear nonhomogeneous non-stationary periodic discrete equation of the first order does not have strongly irregular non-stationary periodic solutions.

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ISSN 1561-2430 (Print)
ISSN 2524-2415 (Online)