scholarly journals Oscillation Criteria for Certain Second Order Difference Equations

1992 ◽  
Vol 11 (3) ◽  
pp. 425-429 ◽  
Author(s):  
E. Thandapani
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Order Difference ◽  
Oscillation Criteria

scholarly journals Oscillation theorems for second order difference equations woth negative neutral term

2015 ◽  
Vol 46 (4) ◽  
pp. 441-451 ◽  
Author(s):  
Ethiraju Thandapani ◽  
Devarajulu Seghar ◽  
Sandra Pinelas
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Second Order ◽  
Neutral Difference Equation ◽  
Order Difference ◽  
Oscillation Criteria ◽  
Neutral Term ◽  
Oscillation Theorems ◽  
Positive Integers

In this paper we obtain some new oscillation criteria for the neutral difference equation \begin{equation*} \Delta \Big(a_n (\Delta (x_n-p_n x_{n-k}))\Big)+q_n f(x_{n-l})=0 \end{equation*} where $0\leq p_n\leq p0$ and $l$ and $k$ are positive integers. Examples are presented to illustrate the main results. The results obtained in this paper improve and complement to the existing results.

scholarly journals Oscillation results for nonlinear second order difference equations with mixed neutral terms

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Said R. Grace ◽  
Jehad Alzabut
Keyword(s):  
Difference Equations ◽  
Wide Class ◽  
Second Order ◽  
Order Difference ◽  
Oscillation Criteria ◽  
First Order ◽  
Oscillatory Behaviors

AbstractIn this paper, we establish new oscillation criteria for nonlinear second order difference equations with mixed neutral terms. The key idea of our approach is to compare with first order equations whose oscillatory behaviors are already known. The obtained results not only improve and extend existing results reported in the literature but also provide a new platform for the investigation of a wide class of nonlinear second order difference equations. The results are supported by examples to demonstrate the validity of the theoretical findings.

scholarly journals Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions

2021 ◽  
Vol 115 (3) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Linear Difference Equations ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

AbstractIn this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian $$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$ Δ ( Δ u ( k - 1 ) p - 2 Δ u ( k - 1 ) ) + a ( k ) u ( k ) p - 2 u ( k ) = 0 with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

Spectrum theory of second-order difference equations with indefinite weight

2018 ◽  
Vol 8 (3) ◽  
pp. 971-985
Author(s):  
Ruyun Ma ◽  
Chenghua Gao ◽  
Yanqiong Lu
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Indefinite Weight ◽  
Order Difference
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