Abstract
We obtain necessary and sufficient conditions so that every solution of neutral delay difference equation Δyn-∑j=1kpnjyn-mj+qnG(yσ(n))=fn oscillates or tends to zero as n→∞, where {qn} and {fn} are real sequences and G∈C(R,R), xG(x)>0, and m1,m2,…,mk are positive integers. Here Δ is the forward difference operator given by Δxn=xn+1-xn, and {σn} is an increasing unbounded sequences with σn≤n. This paper complements, improves, and generalizes some past and recent results.
Highlights
IntroductionWe study the oscillatory behavior of solutions of neutral difference equation (1) under the following assumptions
Consider the neutral delay difference equation of first order kΔ + qnG (yσ(n)) = fn (1)j=1 where Δ is the forward difference operator given by Δxn = xn+1 − xn, qn and fn are members of infinite real sequences, and mj are positive integers
Δ + qnG (yσ(n)) = fn j=1 where Δ is the forward difference operator given by Δxn = xn+1 − xn, qn and fn are members of infinite real sequences, and mj are positive integers
Summary
We study the oscillatory behavior of solutions of neutral difference equation (1) under the following assumptions. The work in this paper complements and generalizes the work in [3, 9] This can be verified that the results in [3, 9] which are concerned with the study of (6) and (7) cannot be applied to the delay difference equation. Note that (10) implies (H4) and (H4) is satisfied in (9) and the results of this paper give an answer to the behavior of solutions of neutral equations like (9). By a solution of (1) we mean a real sequence {yn} which is defined for all positive integers n ≥ ρ and satisfies (1) for n ≥ n0. We assume the existence of solution of (1) and study its oscillatory and asymptotic behavior
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
