scholarly journals Qualitative Behavior of a Nonlinear Generalized Recursive Sequence with Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Tarek F. Ibrahim ◽  
Abdul Qadeer Khan ◽  
Abdelhameed Ibrahim
Keyword(s):  
Difference Equation ◽  
Discrete Time ◽  
Difference Equations ◽  
Qualitative Behavior ◽  
Order Difference ◽  
Discrete Time Systems ◽  
Recursive Sequence ◽  
Order Difference Equation ◽  
Time Systems ◽  
Equation With Delay

Difference equations are of growing importance in engineering in view of their applications in discrete time-systems used in association with microprocessors. We will check out the global stability and boundedness for a nonlinear generalized high-order difference equation with delay.

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.

Observability of linear discrete-time systems of algebraic and difference equations

2017 ◽  
Vol 92 (2) ◽  
pp. 339-355 ◽  
Author(s):  
Lazaros Moysis ◽  
Nicholas Karampetakis ◽  
Efstathios Antoniou
Keyword(s):  
Discrete Time ◽  
Difference Equations ◽  
Discrete Time Systems ◽  
Time Systems

scholarly journals Nonuniform Exponential Trichotomy for Linear Discrete-Time Systems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Xiao-qiu Song ◽  
Tian Yue ◽  
Dong-qing Li
Keyword(s):  
Exponential Stability ◽  
Banach Spaces ◽  
Discrete Time ◽  
Difference Equations ◽  
Exponential Dichotomy ◽  
Linear Difference Equations ◽  
Discrete Time Systems ◽  
Exponential Trichotomy ◽  
Time Systems

The aim of this paper is to give several characterizations for nonuniform exponential trichotomy properties of linear difference equations in Banach spaces. Well-known results for exponential stability and exponential dichotomy are extended to the case of nonuniform exponential trichotomy.

scholarly journals Exponential dichotomies for linear discrete-time systems in Banach spaces

2012 ◽  
Vol 6 (1) ◽  
pp. 140-155 ◽  
Author(s):  
Ioan-Lucian Popa ◽  
Mihail Megan ◽  
Traian Ceauşu
Keyword(s):  
Banach Spaces ◽  
Discrete Time ◽  
Difference Equations ◽  
Linear Difference Equations ◽  
Exponential Dichotomies ◽  
Discrete Time Systems ◽  
Time Systems

In this paper we investigate some dichotomy concepts for linear difference equations in Banach spaces. Characterizations of these concepts are given. Some illustrating examples clarifies the relations between these concepts.

scholarly journals Solution of homogeneous linear difference equations

1980 ◽  
Vol 21 (3) ◽  
pp. 293-296 ◽  
Author(s):  
J. D. Love
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Continued Fraction ◽  
Second Order ◽  
Linear Difference Equations ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
Simple Product ◽  
Homogeneous Linear

AbstractWhen the first two elements of a sequence satisfying a second order difference equation are prescribed, the remaining elements are evaluated from a continued fraction and a simple product.

scholarly journals On (h,k)-Dichotomies for Nonautonomous Linear Difference Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mihai Gabriel Babuţia ◽  
Mihail Megan ◽  
Ioan-Lucian Popa
Keyword(s):  
Banach Spaces ◽  
Discrete Time ◽  
Difference Equations ◽  
Linear Difference Equations ◽  
Discrete Time Systems ◽  
Time Systems

This paper considers two general concepts of dichotomy for noninvertible and nonautonomous linear discrete-time systems in Banach spaces. These concepts use two types of dichotomy projections sequences (invariant and strongly invariant) and generalize some well-known dichotomy concepts (uniform, nonuniform, exponential, and polynomial). In the particular case of strongly invariant dichotomy projections, we present characterizations of these sequences and connections with other dichotomy concepts existent in the literature. Some illustrative examples clarify the implications between these concepts.

scholarly journals Growth of Meromorphic Solutions of Some -Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Guowei Zhang
Keyword(s):  
Difference Equation ◽  
Fixed Points ◽  
Difference Equations ◽  
Meromorphic Solutions ◽  
Order Difference ◽  
Complex Difference ◽  
Complex Difference Equations ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
The Difference

We estimate the growth of the meromorphic solutions of some complex -difference equations and investigate the convergence exponents of fixed points and zeros of the transcendental solutions of the second order -difference equation. We also obtain a theorem about the -difference equation mixing with difference.

scholarly journals TRANSFORMATION OF THE LINEAR DIFFERENCE EQUATION INTO A SYSTEM OF THE FIRST ORDER DIFFERENCE EQUATIONS

2019 ◽  
pp. 76-80
Author(s):  
M.I. Ayzatsky
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Linear Difference Equation ◽  
Second Order ◽  
Dimensional System ◽  
Order Difference ◽  
Order Linear ◽  
First Order ◽  
Second Order Difference Equation ◽  
Order Difference Equation

The transformation of the N-th-order linear difference equation into a system of the first order difference equations is presented. The proposed transformation opens possibility to obtain new forms of the N-dimensional system of the first order equations that can be useful for the analysis of solutions of the N-th-order difference equations. In particular for the third-order linear difference equation the nonlinear second-order difference equation that plays the same role as the Riccati equation for second-order linear difference equation is obtained. The new form of the Ndimensional system of first order equations can also be used to find the WKB solutions of the linear difference equation with coefficients that vary slowly with index.

scholarly journals Sequences of positive homoclinic solutions to difference equations with variable exponent

2020 ◽  
Vol 70 (2) ◽  
pp. 417-430
Author(s):  
Robert Stegliński ◽  
Magdalena Nockowska-Rosiak
Keyword(s):  
Variational Principle ◽  
Difference Equation ◽  
Difference Equations ◽  
Critical Point Theory ◽  
Variable Exponent ◽  
Point Theory ◽  
Homoclinic Solutions ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

Abstract We study the existence of infinitely many positive homoclinic solutions to a second-order difference equation on integers with pk-Laplacian. To achieve our goal we use the critical point theory and the general variational principle of Ricceri.

scholarly journals On The Solutions of Some Difference Equations Systems and Analytical Properties

2018 ◽  
Vol 22 ◽  
pp. 01050
Author(s):  
Münevver Tuz
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Equation System ◽  
Asymptotic Behavior Of Solutions ◽  
Asymptotic Results ◽  
Order Difference ◽  
Positive Balance ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
The Given

In this study, we investigated the global asymptotic behaviors of their solutions by taking the second-order difference equation system. According to the given conditions, we obtained some asymptotic results for the positive balance of the system. We have also worked on q-fast changing functions. Such functions form the class of q-Caramate functions. We have applied q-Caramate functions to linear q-difference equations and We have also learned about the asymptotic behavior of solutions. In addition, we have studied the problem of initial and boundary value for the q-difference equation

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