IJPAM: Volume 57, No. 3 (2009)

CLASSIFICATION OF SOLUTIONS FOR SECOND ORDER
QUASI-LINEAR NEUTRAL DELAY DIFFERENCE EQUATIONS

S. Lourdu Marian$^1$, A. George Maria Selvam$^2$
$^1$Department of Master of Computer Applications
Saveetha Engineering College
Thandalam, Chennai, 602 105, INDIA
e-mail: lm_jerrome@rediffmail.com
$^2$Department of Mathematics
Sacred Heart College
Tirupattur, Vellore Dist., Tamil Nadu, 635 601, INDIA
e-mail: agm_shc@rediffmail.com


Abstract.In this paper, we investigate the oscillatory and non-oscillatory behavior of solutions of second order quasi-linear neutral delay difference equation
\begin{multline*}
\Delta \left[ {a(n)\left\vert {\Delta \left( {x(n) + p(n)x(n...
... \\ +
q(n + 1)f(x(n + 1 - \sigma ))h(\Delta x(n + 1)) = 0 ,
\end{multline*}
where $n \ge n_0, \alpha >0, \tau \ge 0$ and $\sigma \ge 0$ are constants, $a(n),q(n),p(n)$ are positive real sequences and $f,h \in C(\mathbb{R}:\mathbb{R})$.

Received: November 12, 2009

AMS Subject Classification: 39A10, 39A11

Key Words and Phrases: oscillation, quasi-linear, neutral, delay, difference equations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 3