#### Glasnik Matematicki, Vol. 37, No.1 (2002), 119-131.

### OSCILLATORY AND ASYMPTOTIC PROPERTIES OF
SOLUTIONS OF NONLINEAR FOURTH ORDER DIFFERENCE EQUATIONS

### E. Thandapani and I. M. Arockiasamy

Department of Mathematics, Periyar University, Salem - 636011,
Tamilnadu, India

*e-mail:* `ethandapani@yahoo.co.in`

**Abstract.** The authors consider the difference equation

Δ^{2} (*r*_{n} Δ^{2}
*y*_{n})
±
*q*_{n} *f*(*y*_{n}) =
*Q*_{n}; *n* = 1,2,3,...
(*)

where *r*_{n} > 0, *q*_{n} > 0,
for all *n* ≥ 1
and *f* : **R** →
**R**
is continuous such that *u**f*(*u*) > 0 for
*u* ≠ 0.
Dividing the solutions of (*) into several classes for the cases
*Q*_{n} = 0 and *Q*_{n}
≠ 0, the authors obtain
conditions for the existence / nonexistence of solutions of (*)
in these classes. Examples are inserted to illustrate the results.
**2000 Mathematics Subject Classification.**
39A10.

**Key words and phrases.** Difference equation, asymptotic
behavior, nonoscillatory.

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