Theory and Modern Applications
Page 96 of 98
We investigate the periodic nature of solutions of a "max-type" difference equation sometimes referred to as the "Lyness max" equation. The equation we consider is
...
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...
-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...
In this paper, we consider the nonlinear difference equation
,
The authors consider the second-order nonlinear difference equation of the type
using critical point theory, and they obtain some new r...
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...
We consider the half-linear second-order difference equation
,
-Laplacian Difference Equations
We deal with Dirichlet boundary value problems for
-Laplacian difference equations depending on a parameter
...
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 ...
An existence result of multiple periodic solutions to the asymptotically linear discrete Hamiltonian systems is obtained by using the Morse index theory.
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...
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...
We consider the difference equation
,
, in the context of a ...
We study the existence of solutions of nonlinear discrete boundary value problems
,
...
We consider the following system of Lyness-type difference equations:
,
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...
This paper is concerned with the matrix generalization of ultradiscrete systems. Specifically, we establish a matrix generalization of the ultradiscrete fourth Painlevé equation (ud- ...
We consider second-order difference expressions, with complex coefficients, of the form
acting on infinite sequences. The discrete anal...
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...
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.
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...
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...
By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic 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...
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.
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.
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(
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...
We investigate some qualitative behavior of the solutions of the difference equation xn+ = ax n - bx n /(cx x ...
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...
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...
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...
We investigate the asymptotic behavior of nonautonomous discrete dynamical systems governed by the system of difference equations (recursive equations): y j (n+1) = F ...
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...
We study the global behavior of positive solutions of the system of rational difference equations xn+1 = f(yn-q, xn-s), yn+1 = g(xn-t, yn-p), n = 0,1,2,..., where p, q, s, t ∈ {0,1,2,...} with s ≥ t and p ≥ q, th...
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...
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...
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...
We will expand the scope of application of a fixed point theorem due to Krasnosel'skiÄ and Zabreiko to the family of second-order dynamic equations described by uΔΔ(t) = f(u σ (t
The oscillation and asymptotic behavior of the higher-order delay difference equation
, n = 0,1,2,..., are investigated. Some sufficient...
We study the process of multiple Lebesgue integration on time scales. The relationship of the Riemann and the Lebesgue multiple integrals is investigated.
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...
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...
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.
We investigate the global asymptotic behavior of solutions of the system of difference equations xn+1 = (a+x n )/(b+y n ), yn+1 = (d+y ...
For a sequence of bounded linear operators
on a Banach space X, we investigate the characterization of exponential dichotomy of the difference ...
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...
We investigate in this paper the global behavior of the following difference equation:
, n = 0,1,..., under appropriate assumptions, whe...
We consider the stability problem for the difference system x n = Axn-1 + Bxn-k, where A, B are real matrixes and the delay k is a positive integer. In the case A = -I, the equa...
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