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Oscillatory properties of solutions to the system of first-order linear difference equations $\begin{matrix} Δ u_{k} & = q_{k} v_{k} \\ Δ v_{k} & = - p_{k} u_{k + 1}, \end{matrix}$ are studied. It can be regarded as a discrete analogy of the linear Hamiltonian system of differential equations. We establish some new conditions, which provide oscillation of the considered system. Obtained results extend and improve, in certain sense, results presented in Opluštil (2011).

Some open problems on the solutions of the delay difference equation $x_{n + 1} = A / x_{n}^{2} + 1 / x_{n - k}^{p}$ .

Arciero, M., Ladas, G., Schultz, S.W. (1994)

Georgian Mathematical Journal

Some Perturbation Results On Multivalued Difference Equations

J. Schinas, A. Meimaridou (1982)

Publications de l'Institut Mathématique

Some properties of solutions of a class of nonlinear difference equations

Małgorzata Migda, Ewa Schmeidel (1999)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Some roughness results concerning reducibility for linear difference equations.

Papaschinopoulos, Garyfalos (1988)

International Journal of Mathematics and Mathematical Sciences

Special solutions of linear difference equations with infinite delay

Milan Medveď (1994)

Archivum Mathematicum

For the difference equation $(ϵ) x_{n + 1} = A x_{n} + ϵ \sum_{k = - \infty}^{n} R_{n - k} x_{k}$ ,where $x_{n} \in Y, Y$ is a Banach space, $ϵ$ is a parameter and $A$ is a linear, bounded operator. A sufficient condition for the existence of a unique special solution $y = {y_{n}}_{n = - \infty}^{\infty}$ passing through the point $x_{0} \in Y$ is proved. This special solution converges to the solution of the equation (0) as $ϵ \to 0$ .

Spectral deformations of Jacobi operators.

Gerald Teschl (1997)

Journal für die reine und angewandte Mathematik

Spectral properties of the monodromy matrix for Harper equation

Vladimir Buslaev, Alexander Fedotov (1996)

Journées équations aux dérivées partielles

Spektraltheorie linksdefiniter Differenzengleichungssysteme.

Heinz-Dieter Niessen (1975)

Journal für die reine und angewandte Mathematik

Stability and global attractivity for a class of nonlinear delay difference equations.

Dai, Binxiang, Zhang, Na (2005)

Discrete Dynamics in Nature and Society

Stability and local error of difference methods for the solution of the ordinary differential equation of the first order

Petr Voňka (1972)

Aplikace matematiky

Stability of linear dynamic systems on time scales.

Choi, Sung Kyu, Im, Dong Man, Koo, Namjip (2008)

Advances in Difference Equations [electronic only]

Stability of nonlinear $h$ -difference systems with $n$ fractional orders

Małgorzata Wyrwas, Ewa Pawluszewicz, Ewa Girejko (2015)

Kybernetika

In the paper we study the subject of stability of systems with $h$ -differences of Caputo-, Riemann-Liouville- and Grünwald-Letnikov-type with $n$ fractional orders. The equivalent descriptions of fractional $h$ -difference systems are presented. The sufficient conditions for asymptotic stability are given. Moreover, the Lyapunov direct method is used to analyze the stability of the considered systems with $n$ -orders.

Stability of the positive steady-state solutions of systems of nonlinear Volterra difference equations of population models with diffusion and infinite delay.

Shi, B. (2000)

International Journal of Mathematics and Mathematical Sciences

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Displaying 421 – 440 of 519

Some complements of Cauchy's inequality on time scales.

Some discrete Poincaré-type inequalities.

Some new discrete nonlinear delay inequalities and application to discrete delay equations.

Some notes on oscillation of two-dimensional system of difference equations