IJPAM: Volume 57, No. 3 (2009)

CRITERIA FOR OSCILLATION OF A CLASS OF
SECOND ORDER NON-LINEAR FORCED
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 behavior of solutions of the second order non-linear forced difference equation

\begin{displaymath} \Delta [a(n)\phi(\Delta x(n))] + q(n+1 )f(x(n+1)) = r(n). \end{displaymath}

We also obtain sufficient conditions for any non-oscillatory solution $x(n)$ of the above equation satisfying $\mathop {\lim }\limits_{n \to \infty } \inf \left\vert {x(n)} \right\vert = 0$.

Received: November 12, 2009

AMS Subject Classification: 39A10, 39A11

Key Words and Phrases: oscillation, forced, nonlinear, difference equations

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