RECESSIVE, DOMINANT AND SPIRAL BEHAVIOURS OF SOLUTIONS OF CERTAIN CLASS OF GENERALISED DIFFERENCE EQUATIONS
Abstract
In this paper, the authors define spiral solution, spiral source, spiral sink and obtain recessive, dominant and spiral properties of solutions of the generalized difference equation
\begin{equation}{\label{rp01}}
p(k)u(k+\ell)+p(k-\ell)u(k-\ell)=q(k)u(k)\,,
\end{equation}
where the functions $p(k)\neq 0$ and $q(k)$ are complex sequences defined on $N(\ell)$ and $N$ respectively and $\ell$ is any positive integer. Suitable examples are provided to illustrate the main results.
\begin{equation}{\label{rp01}}
p(k)u(k+\ell)+p(k-\ell)u(k-\ell)=q(k)u(k)\,,
\end{equation}
where the functions $p(k)\neq 0$ and $q(k)$ are complex sequences defined on $N(\ell)$ and $N$ respectively and $\ell$ is any positive integer. Suitable examples are provided to illustrate the main results.
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