First Order Linear Difference Equations and Patterns of Periodic Solutions

2018 ◽  
pp. 31-58
Author(s):  
Michael A. Radin
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
Linear Difference Equations ◽  
Order Linear ◽  
First Order

scholarly journals STRONGLY IRREGULAR PERIODIC SOLUTIONS OF THE FIRST-ORDER LINEAR HOMOGENEOUS DISCRETE EQUATION

2018 ◽  
Vol 62 (3) ◽  
pp. 263-267 ◽  
Author(s):  
A. K. Demenchuk
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Prime Numbers ◽  
Discrete Equation ◽  
Linear Difference Equations ◽  
Order Linear ◽  
First Order ◽  
Discrete Equations

 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.

First-Order Linear Difference Equations

2014 ◽  
pp. 47-55
Author(s):  
Ravi P. Agarwal ◽  
Claudio Cuevas ◽  
Carlos Lizama
Keyword(s):  
Difference Equations ◽  
Linear Difference Equations ◽  
Order Linear ◽  
First Order

Oscillation criteria of first order linear difference equations with delay argument

2008 ◽  
Vol 68 (4) ◽  
pp. 994-1005 ◽  
Author(s):  
G.E. Chatzarakis ◽  
R. Koplatadze ◽  
I.P. Stavroulakis
Keyword(s):  
Difference Equations ◽  
Linear Difference Equations ◽  
Oscillation Criteria ◽  
Order Linear ◽  
Delay Argument ◽  
First Order ◽  
Equations With Delay
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