Oscillations in a class of linear difference equations with periodic coefficients

1994 ◽  
Vol 53 (3-4) ◽  
pp. 175-183 ◽  
Author(s):  
CH. G. Philos ◽  
I. K. Purnaras
Keyword(s):  
Difference Equations ◽  
Linear Difference Equations ◽  
Periodic Coefficients

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.

Stability of solutions of linear difference equations with periodic coefficients

1996 ◽  
Vol 64 (5) ◽  
pp. 959-966 ◽  
Author(s):  
Ya. Z. TSYPKIN ◽  
P. C. PARKS ◽  
A. N. VISHNYAKOV ◽  
K. WARWICK
Keyword(s):  
Difference Equations ◽  
Stability Of Solutions ◽  
Linear Difference Equations ◽  
Periodic Coefficients

scholarly journals Linear difference equations, frieze patterns, and the combinatorial Gale transform

2014 ◽  
Vol 2 ◽  
Author(s):  
SOPHIE MORIER-GENOUD ◽  
VALENTIN OVSIENKO ◽  
RICHARD EVAN SCHWARTZ ◽  
SERGE TABACHNIKOV
Keyword(s):  
Projective Space ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Moduli Space ◽  
Gauss Map ◽  
Rational Maps ◽  
Linear Difference Equations ◽  
Periodic Coefficients ◽  
Gale Transform

AbstractWe study the space of linear difference equations with periodic coefficients and (anti)periodic solutions. We show that this space is isomorphic to the space of tame frieze patterns and closely related to the moduli space of configurations of points in the projective space. We define the notion of a combinatorial Gale transform, which is a duality between periodic difference equations of different orders. We describe periodic rational maps generalizing the classical Gauss map.

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.

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