New Oscillation Criteria for H-Difference Equation With Oscillatory Periodic Coefficients

Abstract

In this manuscript, new oscillation criteria are given for solutions of h-order delay difference equation in the equation (1.1). There, four cases of p are considered: for alpha is an element of & Nopf;, as oscillatory periodic sequences with periods 2 alpha,(2 alpha+1), and (alpha+1) and a quickly oscillating sequence such that p(n)p(n+1)<0. It is well-known that coefficient functions have a very important role in the behavior of the solutions of an equation. The coefficient sequence p has been considered as positive sequences in all oscillation criteria so far. But it is considered as oscillatory periodic sequences and quickly oscillatory sequences for the first time in this study. We use a new technique to prove our results. Also, some examples are provided to demonstrate the effectiveness of the main results.