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On oscillation and nonoscillation properties of Emden-Fowler difference equations

Mariella Cecchi, Zuzana Došlá, Mauro Marini (2009)

Open Mathematics

A characterization of oscillation and nonoscillation of the Emden-Fowler difference equation $Δ (a_{n} {|Δ x_{n}|}^{α} s g n Δ x_{n}) + b_{n} {|x_{n + 1}|}^{β} s g n x_{n + 1} = 0$ is given, jointly with some asymptotic properties. The problem of the coexistence of all possible types of nonoscillatory solutions is also considered and a comparison with recent analogous results, stated in the half-linear case, is made.

On oscillation of second order linear difference equations with deviated arguments.

Koplatadze, R., Kvinikadze, G. (1997)

Memoirs on Differential Equations and Mathematical Physics

On oscillatory first order neutral impulsive difference equations

Arun Kumar Tripathy, Gokula Nanda Chhatria (2020)

Mathematica Bohemica

We have established sufficient conditions for oscillation of a class of first order neutral impulsive difference equations with deviating arguments and fixed moments of impulsive effect.

On oscillatory nonlinear fourth-order difference equations with delays

Arun K. Tripathy (2018)

Mathematica Bohemica

In this work, oscillatory behaviour of solutions of a class of fourth-order neutral functional difference equations of the form $Δ^{2} (r (n) Δ^{2} (y (n) + p (n) y (n - m))) + q (n) G (y (n - k)) = 0$ is studied under the assumption $\sum_{n = 0}^{\infty} \frac{n}{r (n)} < \infty .$ New oscillation criteria have been established which generalize some of the existing results in the literature.

On solutions of linear difference equations with infinite delay.

Lakrib, Mustapha (2000)

Southwest Journal of Pure and Applied Mathematics [electronic only]

On some new N-independent-variable discrete inequalities of the Gronwall type.

Yang, En Hao (1986)

International Journal of Mathematics and Mathematical Sciences

On stability zones for discrete-time periodic linear Hamiltonian systems.

Răsvan, Vladimir (2006)

Advances in Difference Equations [electronic only]

On the asymptotics of mean value points for some finite-difference operators.

Nikonorov, Yu.G. (2002)

Sibirskij Matematicheskij Zhurnal

On the behavior of the solutions to autonomous linear difference equations with continuous variable

Christos G. Philos, Ioannis K. Purnaras (2007)

Archivum Mathematicum

Autonomous linear neutral delay and, especially, (non-neutral) delay difference equations with continuous variable are considered, and some new results on the behavior of the solutions are established. The results are obtained by the use of appropriate positive roots of the corresponding characteristic equation.