Abstract
References
- [1] R. P. Agarwal and P. J. Y. Wong, Advanced Topics in Difference Equations, Kluwer Academic Publishers Group, Dordrecht, 1997.
Abstract
\begin{abstract}
In this work, an illustrative discussion has been made on sufficient conditions under which all vector solutions of first order 2-dim nonautonomous neutral delay difference systems of the form
$$\Delta \left[%
\begin{array}{c}
u(\theta)+b(\theta)u(\theta-\kappa)\\
v(\theta)+b(\theta)v(\theta-\kappa) \\
\end{array}%
\right]= \left[%
\begin{array}{cc}
a_{1}(\theta) & a_{2}(\theta) \\
a_{3}(\theta) & a_{4}(\theta) \\
\end{array}%
\right]\left[%
\begin{array}{c}
g_1(u(\theta-\gamma))\\
g_2(v(\theta-\eta)) \\
\end{array}%
\right]+\left[%
\begin{array}{c}
\varphi_1(\theta)\\
\varphi_2(\theta) \\
\end{array}%
\right], \theta\geq\rho$$
are oscillatory, where $\kappa>0,$ $\gamma\geq 0, \eta\geq 0$ are integers, $a_{j}(\theta), j=1,2,3,4, b(\theta), \varphi_{1}(\theta),$ $\varphi_{2}(\theta)$ are sequences of real numbers for $\theta\in\mathbb{N}(\theta_{0})$ and $g_1, g_2\in\mathcal{C}(\mathbb{R}, \mathbb{R})$ are nondecreasing with the properties $\phi g_1(\phi)>0, \psi g_2(\psi)>0$ for $\phi\neq 0, \psi\neq 0.$ We verify our results with the examples.
\end{abstract}
References
- [1] R. P. Agarwal and P. J. Y. Wong, Advanced Topics in Difference Equations, Kluwer Academic Publishers Group, Dordrecht, 1997.
Details
| Primary Language | English |
|---|---|
| Subjects | Ordinary Differential Equations, Difference Equations and Dynamical Systems |
| Journal Section | Mathematics |
| Authors | |
| Early Pub Date | January 27, 2025 |
| Publication Date | |
| Submission Date | October 7, 2024 |
| Acceptance Date | January 12, 2025 |
| Published in Issue | Year 2025 Early Access |