scholarly journals Explicit bounds for third-order difference equations

2006 ◽  
Vol 47 (3) ◽  
pp. 359-366
Author(s):  
Kenneth S. Berenhaut ◽  
Eva G. Goedhart ◽  
Stevo Stević
Keyword(s):  
Recent Work ◽  
Difference Equations ◽  
Wide Class ◽  
Higher Order ◽  
Second Order ◽  
Third Order ◽  
Order Difference ◽  
Explicit Bounds ◽  
Second Order Equations

AbstractThis paper gives explicit, applicable bounds for solutions of a wide class of third-order difference equations with nonconstant coefficients. The techniques used are readily adaptable for higher-order equations. The results extend recent work of the authors for second-order equations.

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.

scholarly journals Oscillation of nonlinear third-order difference equations with mixed neutral terms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jehad Alzabut ◽  
Martin Bohner ◽  
Said R. Grace
Keyword(s):  
Difference Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Order Difference ◽  
New Approach ◽  
Comparison Technique

AbstractIn this paper, new oscillation results for nonlinear third-order difference equations with mixed neutral terms are established. Unlike previously used techniques, which often were based on Riccati transformation and involve limsup or liminf conditions for the oscillation, the main results are obtained by means of a new approach, which is based on a comparison technique. Our new results extend, simplify, and improve existing results in the literature. Two examples with specific values of parameters are offered.

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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