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.

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 Critical Oscillation Constant for Euler Type Half-Linear Differential Equation Having Multi-Different Periodic Coefficients

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Adil Misir ◽  
Banu Mermerkaya
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Order Differential Equation ◽  
Second Order ◽  
Periodic Coefficients ◽  
Second Order Differential Equation ◽  
Linear Differential ◽  
Critical Oscillation ◽  
Oscillation Constant

We compute explicitly the oscillation constant for Euler type half-linear second-order differential equation having multi-different 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.

Conditional oscillation of Riemann-Weber half-linear differential equations with asymptotically almost periodic coefficients

2014 ◽  
Vol 51 (3) ◽  
pp. 303-321
Author(s):  
Petr Hasil ◽  
Michal Veselý
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Almost Periodic ◽  
Periodic Coefficients ◽  
Conditional Oscillation ◽  
Linear Differential ◽  
Asymptotically Almost Periodic ◽  
Oscillation Constant

We analyse the oscillation and non-oscillation of second-order half-linear differential equations with periodic and asymptotically almost periodic coefficients, where the equations have the so-called Riemann-Weber form. For these equations, we find an explicit oscillation constant. Corollaries and examples are mentioned as well.

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