Oscillation criteria for higher order sturm–liouville difference equations*

1998 ◽  
Vol 4 (5) ◽  
pp. 425-450 ◽  
Author(s):  
Ondřej Došlý
Keyword(s):  
Difference Equations ◽  
Higher Order ◽  
Oscillation Criteria ◽  
Sturm Liouville

scholarly journals OSCILLATORY BEHAVIOR OF HIGHER ORDER NONLINEAR DIFFERENCE EQUATIONS

2020 ◽  
Vol 25 (4) ◽  
pp. 522-530
Author(s):  
Said R. Grace ◽  
John R. Graef
Keyword(s):  
Difference Equations ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Nonlinear Difference Equations ◽  
Oscillation Criteria

The authors present some new oscillation criteria for higher order nonlinear difference equations with nonnegative real coefficients of the form ... Both of the cases n even and n odd are considered. They give examples to illustrate their results.

scholarly journals Oscillation criteria for higher-order neutral type difference equations

2020 ◽  
Vol 44 (3) ◽  
pp. 729-738
Author(s):  
Turhan KÖPRÜBAŞI ◽  
Zafer ÜNAL ◽  
Yaşar BOLAT
Keyword(s):  
Difference Equations ◽  
Neutral Type ◽  
Higher Order ◽  
Oscillation Criteria

Oscillation criteria for higher-order nonlinear delay dynamic equations on time scales

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Yaşar Bolat ◽  
Ömer Akin
Keyword(s):  
Difference Equations ◽  
Difference Operator ◽  
Higher Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Linear Delay ◽  
Delay Dynamic Equations ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Nonlinear Delay

AbstractIn this paper, oscillation criteria are obtained for higher-order half-linear delay difference equations involving generalized difference operator of the formwhere ∆

scholarly journals Oscillatory behavior of nonlinear Hilfer fractional difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tuğba Yalçın Uzun
Keyword(s):  
Difference Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
All Solutions ◽  
Alpha Beta

AbstractIn this paper, we study the oscillation behavior for higher order nonlinear Hilfer fractional difference equations of the type $$\begin{aligned}& \Delta _{a}^{\alpha ,\beta }y(x)+f_{1} \bigl(x,y(x+\alpha ) \bigr) =\omega (x)+f_{2} \bigl(x,y(x+ \alpha ) \bigr),\quad x\in \mathbb{N}_{a+n-\alpha }, \\& \Delta _{a}^{k-(n-\gamma )}y(x) \big|_{x=a+n-\gamma } = y_{k}, \quad k= 0,1,\ldots,n, \end{aligned}$$ Δ a α , β y ( x ) + f 1 ( x , y ( x + α ) ) = ω ( x ) + f 2 ( x , y ( x + α ) ) , x ∈ N a + n − α , Δ a k − ( n − γ ) y ( x ) | x = a + n − γ = y k , k = 0 , 1 , … , n , where $\lceil \alpha \rceil =n$ ⌈ α ⌉ = n , $n\in \mathbb{N}_{0}$ n ∈ N 0 and $0\leq \beta \leq 1$ 0 ≤ β ≤ 1 . We introduce some sufficient conditions for all solutions and give an illustrative example for our results.

On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers

2020 ◽  
Vol 70 (3) ◽  
pp. 641-656
Author(s):  
Amira Khelifa ◽  
Yacine Halim ◽  
Abderrahmane Bouchair ◽  
Massaoud Berkal
Keyword(s):  
General Solution ◽  
Closed Form ◽  
Difference Equations ◽  
Fibonacci Numbers ◽  
Higher Order ◽  
Real Numbers ◽  
Lucas Numbers ◽  
Rational Difference Equations ◽  
Initial Values ◽  
Fibonacci And Lucas Numbers

AbstractIn this paper we give some theoretical explanations related to the representation for the general solution of the system of the higher-order rational difference equations$$\begin{array}{} \displaystyle x_{n+1} = \dfrac{1+2y_{n-k}}{3+y_{n-k}},\qquad y_{n+1} = \dfrac{1+2z_{n-k}}{3+z_{n-k}},\qquad z_{n+1} = \dfrac{1+2x_{n-k}}{3+x_{n-k}}, \end{array}$$where n, k∈ ℕ0, the initial values x−k, x−k+1, …, x0, y−k, y−k+1, …, y0, z−k, z−k+1, …, z1 and z0 are arbitrary real numbers do not equal −3. This system can be solved in a closed-form and we will see that the solutions are expressed using the famous Fibonacci and Lucas numbers.

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