STRONGLY IRREGULAR PERIODIC SOLUTIONS OF THE FIRST-ORDER LINEAR HOMOGENEOUS DISCRETE EQUATION
https://doi.org/10.29235/1561-8323-2018-62-3-263-267
Abstract
In 1950 J. Massera proved that a fi rst-order scalar periodic ordinary differential equation has no strongly ira proved that a first-order scalar periodic ordinary differential equation has no strongly irregular periodic solutions, that is, such solutions whose period of solution is incommensurable with the period of equation. For difference equations with discrete time, strong irregularity means that the period of the equation and the period of its solution are relatively prime numbers. It is known that in the case of discrete equations, the above result of J. Massera has no complete analog.
The purpose of this article is to investigate the possibility to realize Massera’s theorem for certain classes of difference equations. To do this, we consider the class of linear difference equations. It is proved that a first-order linear homogeneous non-stationary periodic discrete equation has no strongly irregular non-stationary periodic solutions.
About the Author
A. K. Demenchuk
Institute of Mathematics of the National Academy of Science of Belarus.
Belarus
Belarus
Demenchuk Aleksandr Konstantinovich – D. Sc. (Physics and Mathematics), Assistant Professor, Leading Researcher.
11, Surganov Str., 220072, Minsk.
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