# OSCILLATION THEORY FOR A CLASS OF SECOND ORDER QUASILINEAR DIFFERENCE EQUATIONS

## DOI:

https://doi.org/10.5556/j.tkjm.28.1997.4319## Keywords:

Nonoscillatory solutions, oscillation, quasilinear difference cqua tions## Abstract

In this paper the authors establish necessary and sufficient conditons for the second order quasilinear difference equation

\[\Delta (\alpha_n(\Delta y_n)^{\alpha*})+f(n, y_{n+1})=0\qquad\qquad n\in N(n_0)\qquad\qquad \text{(E)}\]

to have various types of nonoscillatory solutions. In addition, in the case when (E) is either strongly superlinear or strongly sublinear, they establish necessary and su伍 c1ent conditions for all solutions to oscillate.

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*Tamkang Journal of Mathematics*,

*28*(3), 229-238. https://doi.org/10.5556/j.tkjm.28.1997.4319

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