IJPAM: Volume 54, No. 4 (2009)

MATLAB APPLICATIONS OF THE OSCILLATIONS
OF FORCED NEUTRAL DIFFERENCE EQUATIONS WITH
POSITIVE AND NEGATIVE COEFFICIENTS

M. Maria Susai Manuel$^1$, A. George Maria Selvam$^2$, M. Paul Loganathan$^3$
$^{1,2}$Department of Mathematics
Sacred Heart College
Vellore Dist., Tirupattur, 635 601, Tamil Nadu, INDIA
$^3$Governmental High School, Oddappatti
Krishnagiri, 635 203, Tamil Nadu, INDIA
e-mail: manuelmsm_03@yahoo.co.in


Abstract.In this paper, the authors investigate the oscillation of forced neutral difference equation with positive and negative coefficients of the form

\begin{displaymath} \Delta(x_n-c_n x_{n-r}) + p_n x_{n-k} - q_n x_{n-\ell} = e_n,\quad n\geq n_0 \end{displaymath}

where $p_n, q_n, c_n, e_n \: (n=0,1,2\dots)$ are real numbers with $p_n\geq0$, $q_n\geq 0$, $c_n\geq0, \: e_n \in \mathbb{R},k,\ell$ and $r$ are integers with $0 \leq \ell \leq k-1, r>0, h_n = p_n - q_{n-k+\ell}\geq 0$ and not identically zero. Suitable examples are provided to illustrate the results and the trajectories of solutions are obtained using MATLAB.

Received: June 10, 2009

AMS Subject Classification: 39A10, 39A11

Key Words and Phrases: difference equations, forced, neutral, oscillation, positive and negative coefficients

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 4