IJPAM: Volume 1, No. 4 (2002)

OSCILLATION OF NONLINEAR NEUTRAL
DELAY DIFFERENCE EQUATIONS

S.H. SakerFaculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznan, POLAND
Mathematics Dept.
Faculty of Science
Mansoura University
Mansoura 35516, EGYPT
e-mail: shsaker@mum.mans.edu.eg
and
Faculty of Mathematics and Computer Science
Adam Mickiewicz University
Matejki 48/49, 60-769 Poznan, POLAND
e-mail: shsaker@amu.edu.pl


Abstract.We present new sufficient conditions for oscillation of all solutions of the nonlinear neutral delay difference equation

\begin{displaymath}
\Delta (y_{n}-p_{n}y_{n-\tau })+q_{n}\prod\limits_{i=1}^{m}...
...^{\alpha _{i}}\sgn y_{n-\delta _{i}}=0,\quad n=0,1,2, \dots .
\end{displaymath}

where { $p_{n}\}_{n=0}^{\infty }$ and { $q_{n}\}_{n=0}^{\infty }$ are sequences of positive real numbers, $\tau $ and $\delta _{i}$ for $i=1,2, \dots ,m$ are nonnegative integers. Our results improve some of the well known oscillation results in the literature.

Received: March 19, 2002

AMS Subject Classification: 39A10

Key Words and Phrases: oscillation, neutral delay difference equations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 1
Issue: 4