Oscillatory Behavior of Higher Order Nonlinear Mixed Type Difference Equations With a Nonlinear Neutral Term
DOI:
https://doi.org/10.24297/jam.v22i.9484Keywords:
oscillation, nonlinear, high order, Difference equationAbstract
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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