Articles

Absolute Stability of Discrete-Time Systems with Delay

We investigate the stability of nonlinear nonautonomous discrete-time systems with delaying arguments, whose linear part has slowly varying coefficients, and the nonlinear part has linear majorants. Based on t...

Authors: Rigoberto Medina

-Genocchi Numbers and Polynomials Associated with -Genocchi-Type -Functions

The main purpose of this paper is to study on generating functions of the -Genocchi numbers and polynomials. We prove new relation for t...

Authors: Yilmaz Simsek, Ismail Naci Cangul, Veli Kurt and Daeyeoul Kim

The Periodic Character of the Difference Equation

In this paper, we consider the nonlinear difference equation ,

Authors: Taixiang Sun and Hongjian Xi

Existence Theorems of Periodic Solutions for Second-Order Nonlinear Difference Equations

The authors consider the second-order nonlinear difference equation of the type using critical point theory, and they obtain some new r...

Authors: Xiaochun Cai and Jianshe Yu

Dynamical Properties for a Class of Fourth-Order Nonlinear Difference Equations

We consider the dynamical properties for a kind of fourth-order rational difference equations. The key is for us to find that the successive lengths of positive and negative semicycles for nontrivial solutions...

Authors: Dongsheng Li, Pingping Li and Xianyi Li

Linearized Riccati Technique and (Non-)Oscillation Criteria for Half-Linear Difference Equations

We consider the half-linear second-order difference equation ,

Authors: Ondřej Došlý and Simona Fišnarová

Three Solutions to Dirichlet Boundary Value Problems for -Laplacian Difference Equations

We deal with Dirichlet boundary value problems for -Laplacian difference equations depending on a parameter ...

Authors: Liqun Jiang and Zhan Zhou

Linear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space

A class of the linear impulsive periodic system with time-varying generating operators on Banach space is considered. By constructing the impulsive evolution operator, the existence of ...

Authors: Jin Rong Wang, X. Xiang and W. Wei

Multiple Periodic Solutions to Nonlinear Discrete Hamiltonian Systems

An existence result of multiple periodic solutions to the asymptotically linear discrete Hamiltonian systems is obtained by using the Morse index theory.

Authors: Bo Zheng

Variationally Asymptotically Stable Difference Systems

We characterize the h-stability in variation and asymptotic equilibrium in variation for nonlinear difference systems via n_∞-summable similarity and comparison principle. Furthermore we study the asymptotic equiv...

Authors: Sung Kyu Choi, Yoon Hoe Goo and Namjip Koo

Necessary Conditions of Optimality for Second-Order Nonlinear Impulsive Differential Equations

We discuss the existence of optimal controls for a Lagrange problem of systems governed by the second-order nonlinear impulsive differential equations in infinite dimensional spaces. We apply a direct approach...

Authors: Y. Peng, X. Xiang and W. Wei

Oscillatory Solutions for Second-Order Difference Equations in Hilbert Spaces

We consider the difference equation , , in the context of a ...

Authors: Cristóbal González and Antonio Jiménez-Melado

Unbounded Perturbations of Nonlinear Second-Order Difference Equations at Resonance

We study the existence of solutions of nonlinear discrete boundary value problems , ...

Authors: Ruyun Ma

On a k-Order System of Lyness-Type Difference Equations

We consider the following system of Lyness-type difference equations: ,

Authors: G. Papaschinopoulos, C. J. Schinas and G. Stefanidou

On the Integrability of Quasihomogeneous Systems and Quasidegenerate Infinity Systems

The integrability of quasihomogeneous systems is considered, and the properties of the first integrals and the inverse integrating factors of such systems are shown. By solving the systems of ordinary differen...

Authors: Yanxia Hu

An Ultradiscrete Matrix Version of the Fourth Painlevé Equation

This paper is concerned with the matrix generalization of ultradiscrete systems. Specifically, we establish a matrix generalization of the ultradiscrete fourth Painlevé equation (ud- ...

Authors: Chris M. Field and Chris M. Ormerod

Relations between Limit-Point and Dirichlet Properties of Second-Order Difference Operators

We consider second-order difference expressions, with complex coefficients, of the form acting on infinite sequences. The discrete anal...

Authors: A. Delil

Exponential Stability for Impulsive BAM Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms

Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global...

Authors: Qiankun Song and Jinde Cao

Periodic Solutions for Subquadratic Discrete Hamiltonian Systems

Some existence conditions of periodic solutions are obtained for a class of nonautono mous subquadratic first-order discrete Hamiltonian systems by the minimax methods in the critical point theory.

Authors: Xiaoqing Deng

Mean Square Summability of Solution of Stochastic Difference Second-Kind Volterra Equation with Small Nonlinearity

Stochastic difference second-kind Volterra equation with continuous time and small nonlinearity is considered. Via the general method of Lyapunov functionals construction, sufficient conditions for uniform mea...

Authors: Beatrice Paternoster and Leonid Shaikhet

Convergence of a Mimetic Finite Difference Method for Static Diffusion Equation

The numerical solution of partial differential equations with finite differences mimetic methods that satisfy properties of the continuum differential operators and mimic discrete versions of appropriate integ...

Authors: J. M. Guevara-Jordan, S. Rojas, M. Freites-Villegas and J. E. Castillo

Oscillation Criteria for Second-Order Delay Dynamic Equations on Time Scales

By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations

Authors: Zhenlai Han, Bao Shi and Shurong Sun

Asymptotic Expansions for Higher-Order Scalar Difference Equations

We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic descri...

Authors: Ravi P. Agarwal and Mihály Pituk

Existence of Periodic and Subharmonic Solutions for Second-Order p-Laplacian Difference Equations

We obtain a sufficient condition for the existence of periodic and subharmonic solutions of second-order p-Laplacian difference equations using the critical point theory.

Authors: Peng Chen and Hui Fang

Periodic and Almost Periodic Solutions of Functional Difference Equations with Finite Delay

For periodic and almost periodic functional difference equations with finite delay, the existence of periodic and almost periodic solutions is obtained by using stability properties of a bounded solution.

Authors: Yihong Song

Multiple nonnegative solutions for BVPs of fourth-order difference equations

First, existence criteria for at least three nonnegative solutions to the following boundary value problem of fourth-order difference equation Δ⁴x(t-2) = a(t)f(x(t)),t ∈ [2, T], x(0) = x(T + 2) = 0, Δ²x(0) = Δ²x(

Authors: Jian-Ping Sun

Optimization Of discrete and differential inclusions of Goursat-Darboux type with state constraints

Necessary and sufficient conditions of optimality under the most general assumptions are deduced for the considered and for discrete approximation problems. Formulation of sufficient conditions for differentia...

Authors: Elimhan N Mahmudov

On the Difference equation x_n+ = ax _n - bx _n /(cx _x - dx_n-1)

We investigate some qualitative behavior of the solutions of the difference equation x_n+ = ax _n - bx _n /(cx _{x ...}

Authors: EM Elabbasy, H El-Metwally and EM Elsayed

Boundedness and vanishing of solutions for a forced delay dynamic equation

We give conditions under which all solutions of a time-scale first-order nonlinear variable-delay dynamic equation with forcing term are bounded and vanish at infinity, for arbitrary time scales that are unbou...

Authors: Douglas R Anderson

Boundedness in functional dynamic equations on time scales

Using nonnegative definite Lyapunov functionals, we prove general theorems for the boundedness of all solutions of a functional dynamic equation on time scales. We apply our obtained results to linear and nonl...

Authors: Elvan Akin-Bohner and Youssef N Raffoul

Convergence and periodicity of solutions for a class of difference systems

A class of difference systems of artificial neural network with two neurons is considered. Using iterative technique, the sufficient conditions for convergence and periodicity of solutions are obtained in seve...

Authors: Honghua Bin, Lihong Huang and Guang Zhang

On nonautonomous discrete dynamical systems driven by means

We investigate the asymptotic behavior of nonautonomous discrete dynamical systems governed by the system of difference equations (recursive equations): y _j (n+1) = F _...

Authors: Raghib M Abu-Saris

Asymptotic stability for dynamic equations on time scales

We examine the conditions of asymptotic stability of second-order linear dynamic equations on time scales. To establish asymptotic stability we prove the stability estimates by using integral representations o...

Authors: Gro Hovhannisyan

On the system of rational difference equations x_n+1 = f(y_n-q, x_n-s), y_n+1 = g(x_n-t, y_n-p)

We study the global behavior of positive solutions of the system of rational difference equations x_n+1 = f(y_n-q, x_n-s), y_n+1 = g(x_n-t, y_n-p), n = 0,1,2,..., where p, q, s, t ∈ {0,1,2,...} with s ≥ t and p ≥ q, th...

Authors: Taixiang Sun and Hongjian Xi

A remark on k th-order linear functional equations with constant coefficients

Abel functional equations are associated to a linear homogeneous functional equation with constant coefficients. The work uses the space S of continuous strictly monotonic functions. Generalized terms are used, b...

Authors: Jitka Laitochová

Extending generalized Fibonacci sequences and their binet-type formula

We study the extension problem of a given sequence defined by a finite order recurrence to a sequence defined by an infinite order recurrence with periodic coefficient sequence. We also study infinite order re...

Authors: Mustapha Rachidi and Osamu Saeki

On lower and upper solutions without ordering on time scales

In order to enlarge the set of boundary value problems on time scales, for which we can use the lower and upper solutions technique to get existence of solutions, we extend this method to the case when the pai...

Authors: Petr Stehlík

Dynamic equations and applications

Authors: Martin Bohner and Allan Peterson

An existence result for a multipoint boundary value problem on a time scale

We will expand the scope of application of a fixed point theorem due to Krasnosel'skiĭ and Zabreiko to the family of second-order dynamic equations described by u^ΔΔ(t) = f(u ^σ (t

Authors: Basant Karna and Bonita A Lawrence

Oscillation of higher-order delay difference equations

The oscillation and asymptotic behavior of the higher-order delay difference equation , n = 0,1,2,..., are investigated. Some sufficient...

Authors: Yinggao Zhou

Multiple Lebesgue integration on time scales

We study the process of multiple Lebesgue integration on time scales. The relationship of the Riemann and the Lebesgue multiple integrals is investigated.

Authors: Martin Bohner and Gusein Sh Guseinov

Using supermodels in quantum optics

Starting from supersymmetric quantum mechanics and related supermodels within Schrödinger theory, we review the meaning of self-similar superpotentials which exhibit the spectrum of a geometric series. We cons...

Authors: Nicole Garbers and Andreas Ruffing

Existence results for φ-Laplacian boundary value problems on time scales

This paper is devoted to proving the existence of the extremal solutions of a φ-Laplacian dynamic equation coupled with nonlinear boundary functional conditions that include as a particular case the Dirichlet and...

Authors: Alberto Cabada

Existence for a class of discrete hyperbolic problems

We investigate the existence and uniqueness of solutions to a class of discrete hyperbolic systems with some nonlinear extreme conditions and initial data, in a real Hilbert space.

Authors: Rodica Luca

Asymptotic behavior of a competitive system of linear fractional difference equations

We investigate the global asymptotic behavior of solutions of the system of difference equations x_n+1 = (a+x _n )/(b+y _n ), y_n+1 = (d+y _...

Authors: MRS Kulenović and M Nurkanović

Exponential dichotomy of difference equations in l _p -phase spaces on the half-line

For a sequence of bounded linear operators on a Banach space X, we investigate the characterization of exponential dichotomy of the dif...

Authors: Nguyen Thieu Huy and Vu Thi Ngoc Ha

Perturbation method for linear difference equations with small parameters

We consider a boundary value problem for a linear difference equation with several widely different coefficients. We study the existence and uniqueness of its solution and we give successive asymptotic approxi...

Authors: Tahia Zerizer

Global behavior of a higher-order rational difference equation

We investigate in this paper the global behavior of the following difference equation: , n = 0,1,..., under appropriate assumptions, whe...

Authors: Hongjian Xi and Taixiang Sun

Stability of a delay difference system

We consider the stability problem for the difference system x _n = Ax_n-1 + Bx_n-k, where A, B are real matrixes and the delay k is a positive integer. In the case A = -I, the equa...

Authors: Mikhail Kipnis and Darya Komissarova

Hille-Kneser-type criteria for second-order dynamic equations on time scales

We consider the pair of second-order dynamic equations, (r(t)(x^Δ) ^γ )^Δ + p(t)x ^γ (t) = 0 and (r(t)(x^Δ) ^γ )^Δ +

Authors: L Erbe, A Peterson and SH Saker