ON OSCILLATORY NONLINEAR 2-D NEUTRAL DYNAMIC SYSTEMS ON TIME SCALES
ARUN KUMAR akt TRIPATHY
Sambalpur University India
Co-Author(s): Shibanee Sahu
Abstract:
\noindent
\noindent
This work is concerned with the oscillation results of a class of 2-D neutral dynamic system of the form:
\begin{align*}
\begin{bmatrix}
u(t)+p(t)u(t-\tau)\\
v(t)+p(t)v(t-\tau) \\
\end{bmatrix}
^{\Delta}=
\begin{bmatrix}
a_{1}(t) &\ a_{2}(t) \\
a_{3}(t) &\ a_{4}(t) \\
\end{bmatrix}
\begin{bmatrix}
\phi_{1}(u(t-\alpha))\\
\phi_{2}(v(t-\beta))\\
\end{bmatrix}
\end{align*}
on time scales $\mathbb{T},$ where $a_{1}(t), a_{2}(t), a_{3}(t), a_{4}(t), p(t)$ are real valued $rd-continuous$ functions defined on $\mathbb{T}$ such that $|p(t)|0\ and\ r\phi_{2}(r)$ $>0\ for\ r\ne 0,$ and for every right dense point $r$ in $\mathbb{T}$.
\noindent {\bf Keywords:} Oscillation, nonoscillation, time scales, Krasnoselskii`s fixed point theorem.
