# Oscillatory Behavior of Higher Order Nonlinear Mixed Type Difference Equations With a Nonlinear Neutral Term

## DOI:

https://doi.org/10.24297/jam.v22i.9484## Keywords:

oscillation, nonlinear, high order, Difference equation## Abstract

This paper discusses higher order nonlinear neutral mixed type difference equations of the form

Δ^{m}[x(n)+p(n)h(x(σ(n)))]+q(n)f(x(τ(n)))=0, n=0,1,2,…,

where (p(n)), (q(n)) are sequences of nonnegative real numbers, h, f:R→R are continuous and nondecreasing with uh(u)>0, uf(u)>0 for all u≠0, and (σ(n)) and (τ(n)) are sequences of integers such that

lim_{n→∞}τ(n)=lim_{n→∞}σ(n)=∞.

In general, we will examine the oscillatory behavior of the solutions for the above equation. Especially, when m is even, the result obtained here complements studies related to the oscillation of the above equation. In addition, examples showing the accuracy of the results are given.

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*JOURNAL OF ADVANCES IN MATHEMATICS*,

*22*, 30–39. https://doi.org/10.24297/jam.v22i.9484

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Copyright (c) 2023 Ali Çakır, ozkan ocalan, Mustafa Kemal Yıldız

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