IJPAM: Volume 6, No. 2 (2003)

OSCILLATORY AND ASYMPTOTIC BEHAVIOR
OF SECOND ORDER NEUTRAL TYPE
DIFFERENCE EQUATIONS

E. Thandapani$^1$, K. Mahalingam$^2$, John R. Graef$^3$
$^{1,2}$Department of Mathematics
Peryiar University
Salem-636011, Tamilnadu, INDIA
$^1$e-mail: ethandapani@yahoo.co.in
$^3$Department of Mathematics
University of Tennessee at Chattanooga
615 McCallie Avenue
Chattanooga, TN 37403 - 2598, USA
e-mail: john-graef@utc.edu


Abstract.In this paper the authors establish some new criteria for the oscillation of all solutions of the equation

\begin{displaymath} \D^2(x_{n} + ax_{n-k} - bx_{n+\ell}) = q_nx_{n-m}+p_nx_{n+r}\,, \end{displaymath}

and asymptotic behavior of nonoscillatory solutions of the equation

\begin{displaymath}\D^2(x_n-px_{n-k})+Q_nx_{n+1+r}=0.\end{displaymath}

Examples are inserted to illustrate the results.

Received: March 25, 2003

AMS Subject Classification: 39A10

Key Words and Phrases: neutral equations, comparison theorems, oscillation, convergence to zero

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 6
Issue: 2