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.
Keywords
Supporting agencies: The work was carried out at the Institute of Mathematics of the National Academy of Sciences of Belarus within the framework of the Special Project of Fundamental and Applied Scientific Research of the National Academy of Sciences of Belarus “Investigation of the properties of the spectra of discrete systems under perturbations of their coefficients”.
About the Author
A. K. Demenchuk
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Aleksandr K. Demenchuk – Dr. Sc. (Physics and Mathematics), Assistant Professor, Chief Researcher of the Department of Differential Equations
11, Surganova Str., Minsk, 220072
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