Oscillatory behavior of second order unstable type neutral difference equations

Abstract

This paper deals with the oscillatory behavior of all bounded/ unbounded solutions of second order neutral type difference equation of the form

$$ \Delta (a_n(\Delta_c y_n+py_{n-k}))^\alpha)-g_nf(y_{\sigma(n)})=0, $$

where $ p $ is real, $ \alpha $ is a ratio of odd positive integers, $ k $ is a positive integer and $ \{\sigma(n)\} $ is a sequence of integers. Examples are provided to illustrate the results.