Oscillatory Behavior of Higher Order Nonlinear Mixed Type Difference Equations With a Nonlinear Neutral Term - Çakır, Ali; ocalan, ozkan; Yıldız, Mustafa Kemal (JOURNAL OF ADVANCES IN MATHEMATICS, 2023)
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.