IJPAM: Volume 58, No. 1 (2010)

ASYMPTOTIC BEHAVIOR OF NON-OSCILLATORY
SOLUTIONS OF CERTAIN SECOND ORDER
NON-LINEAR 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, S. INDIA
e-mail: lm_jerrome@rediffmail.com
$^2$Department of Mathematics
Sacred Heart College
Tirupattur, 635 601, Vellore Dist., S. INDIA
e-mail: agm_shc@rediffmail.com


Abstract.In this paper, we investigate the asymptotic behavior of all non-oscillatory solutions of the second order non-linear difference equation

\begin{displaymath}
\Delta [p(n)\phi(\Delta x(n))] + q(n+1 )f(x(n+1)) = 0,\quad n \ge n_0.
\end{displaymath}

Also we provide conditions under which $\Delta x(n)$ is oscillatory whenever $x(n)$ is a solution of the above equation. Suitable examples are provided to illustrate the results.

Received: December 12, 2009

AMS Subject Classification: 39A10, 39A11

Key Words and Phrases: asymptotic behavior, oscillation, non-linear, difference equations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 58
Issue: 1