Asymptotic Properties of Nonoscillatory Solutions of Third-Order Delay Difference Equations

Gleska, Alina; Migda, Małgorzata

doi:10.1007/978-3-319-75647-9_27

Cited by 2 publications

(2 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Compared to this, the study of higher-order difference equations receives considerably less attention in literature. Some recent results for the oscillation of third-order difference equations can be found in [3,6,7,9,12,13,24,25], and for fourthorder in [4,10,16,18,23]. In particular, in [7] and [13], the authors studied oscillation and asymptotic properties of solutions of the three-term difference equation…”

Section: Introductionmentioning

confidence: 99%

Oscillation results via comparison theorems for fourth-order delay three-terms difference equations

et al. 2022

Self Cite

View full text Add to dashboard Cite

In this paper we establish sufficient conditions for the oscillation of all solutions of equation $$\begin{aligned} \varDelta ^4x(n)+p(n)\varDelta x(n+1)+q(n)x(n-\tau )=0 \end{aligned}$$ Δ 4 x ( n ) + p ( n ) Δ x ( n + 1 ) + q ( n ) x ( n - τ ) = 0 via comparison with some first order delay difference equations whose oscillatory characters are known. The presented criterion is easily verifiable. Examples are also given to illustrate the main result.

show abstract

Section: Introductionmentioning

confidence: 99%

Oscillation results via comparison theorems for fourth-order delay three-terms difference equations

et al. 2022

Self Cite

View full text Add to dashboard Cite

show abstract

“…Such a method was also used to the discrete counterpart of equation (4). For example, in [13] asymptotic properties of nonoscillatory solutions of the equation…”

Section: Introductionmentioning

confidence: 99%

Asymptotic properties of solutions of third order difference equations

Migda

Nockowska-Rosiak

2020

APPL ANAL DISCRETE M

Self Cite

View full text Add to dashboard Cite

We consider the difference equation of the form ∆(rn∆(pn∆xn)) = anf (x σ(n)) + bn. We present sufficient conditions under which, for a given solution y of the equation ∆(rn∆(pn∆yn)) = 0, there exists a solution x of the nonlinear equation with the asymptotic behavior xn = yn + zn, where z is a sequence convergent to zero. Our approach allows us to control the degree of approximation, i.e., the rate of convergence of the sequence z. We examine two types of approximation: harmonic approximation when zn = o(n s), s ≤ 0, and geometric approximation when zn = o(µ n), µ ∈ (0, 1).

show abstract

Asymptotic Properties of Nonoscillatory Solutions of Third-Order Delay Difference Equations

Cited by 2 publications

References 14 publications

Oscillation results via comparison theorems for fourth-order delay three-terms difference equations

Oscillation results via comparison theorems for fourth-order delay three-terms difference equations

Asymptotic properties of solutions of third order difference equations

Contact Info

Product

Resources

About