The method of Lyapunov functions for systems of linear difference equations with almost periodic coefficients

1996 ◽  
Vol 37 (1) ◽  
pp. 147-150 ◽  
Author(s):  
O. V. Kirichenova ◽  
A. S. Kotyurgina ◽  
R. K. Romanovskiî
Keyword(s):  
Difference Equations ◽  
Lyapunov Functions ◽  
Almost Periodic ◽  
Linear Difference Equations ◽  
Periodic Coefficients

scholarly journals Oscillation and Nonoscillation of Asymptotically Almost Periodic Half-Linear Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Michal Veselý ◽  
Petr Hasil
Keyword(s):  
Difference Equations ◽  
Riccati Transformation ◽  
Almost Periodic ◽  
Linear Difference Equations ◽  
Periodic Coefficients ◽  
Asymptotically Almost Periodic ◽  
Oscillation And Nonoscillation

We analyse half-linear difference equations with asymptotically almost periodic coefficients. Using the adapted Riccati transformation, we prove that these equations are conditionally oscillatory. We explicitly find a constant, determined by the coefficients of a given equation, which is the borderline between the oscillation and the nonoscillation of the equation. We also mention corollaries of our result with several examples.

Reducibility of linear systems of difference equations with almost periodic coefficients

1993 ◽  
Vol 45 (12) ◽  
pp. 1869-1877
Author(s):  
Yu. A. Mitropol'skii ◽  
D. I. Martynyuk ◽  
V. I. Tynnyi
Keyword(s):  
Linear Systems ◽  
Difference Equations ◽  
Almost Periodic ◽  
Periodic Coefficients

scholarly journals Some roughness results concerning reducibility for linear difference equations

1988 ◽  
Vol 11 (4) ◽  
pp. 793-804 ◽  
Author(s):  
Garyfalos Papaschinopoulos
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Exponential Dichotomy ◽  
Coefficient Matrix ◽  
Linear Difference Equation ◽  
Almost Periodic ◽  
Linear Difference Equations ◽  
Joint Property

In this paper we prove first that the exponential dichotomy of linear difference equations is “rough”. Moreover we prove that if the coefficient matrix of a linear difference equation is almost periodic, then the Joint property of having an exponential dichotomy with a projectionPand being reducible withPby an almost periodic kinematics similarity is “rough”.

scholarly journals Critical Oscillation Constant for Difference Equations with Almost Periodic Coefficients

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Petr Hasil ◽  
Michal Veselý
Keyword(s):  
Euler Equation ◽  
Difference Equations ◽  
Almost Periodic ◽  
Periodic Coefficients ◽  
Sturm Liouville ◽  
Critical Oscillation ◽  
Oscillation Constant

We investigate a type of the Sturm-Liouville difference equations with almost periodic coefficients. We prove that there exists a constant, which is the borderline between the oscillation and the nonoscillation of these equations. We compute this oscillation constant explicitly. If the almost periodic coefficients are replaced by constants, our result reduces to the well-known result about the discrete Euler equation.

scholarly journals Bounded solutions of self-adjoint second order linear difference equations with periodic coeffients

2018 ◽  
Vol 16 (1) ◽  
pp. 75-82 ◽  
Author(s):  
A.M. Encinas ◽  
M.J. Jiménez
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Bounded Solutions ◽  
Linear Difference Equations ◽  
Periodic Coefficients ◽  
Order Linear ◽  
Mathieu Equations

AbstractIn this work we obtain easy characterizations for the boundedness of the solutions of the discrete, self–adjoint, second order and linear unidimensional equations with periodic coefficients, including the analysis of the so-called discrete Mathieu equations as particular cases.

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