1. bookVolume 79 (2021): Issue 2 (December 2021)
Journal Details
License
Format
Journal
eISSN
1338-9750
First Published
12 Nov 2012
Publication timeframe
3 times per year
Languages
English
access type Open Access

Oscillation Tests for Linear Difference Equations with Non-Monotone Arguments

Published Online: 01 Jan 2022
Volume & Issue: Volume 79 (2021) - Issue 2 (December 2021)
Page range: 81 - 100
Received: 23 Aug 2020
Journal Details
License
Format
Journal
eISSN
1338-9750
First Published
12 Nov 2012
Publication timeframe
3 times per year
Languages
English
Abstract

This paper presents sufficient conditions involving limsup for the oscillation of all solutions of linear difference equations with general deviating argument of the form Δx(n)+p(n)x(τ(n))=0,n0[x(n)q(n)x(σ(n))=0,n],\[\Delta x(n) + p(n)x(\tau (n)) = 0,\,n \in {_0}\quad [\nabla x(n) - q(n)x(\sigma (n)) = 0,\,n \in ],\ , where (p(n))n0 and (q(n))n1 are sequences of nonnegative real numbers and (τ(n))n0,(σ(n))n1\[{(\tau (n))_{n \ge 0}},\quad {(\sigma (n))_{n \ge 1}}\] are (not necessarily monotone) sequences of integers. The results obtained improve all well-known results existing in the literature and an example, numerically solved in MATLAB, illustrating the significance of these results is provided.

Keywords

[1] BRAVERMAN, E.—CHATZARAKIS, G.E.—STAVROULAKIS, I. P.: Iterative oscillation tests for difference equations with several non-monotone arguments, J. Difference Equ. Appl. 21 (2015), no. 9, 854–874. Search in Google Scholar

[2] E. BRAVERMAN, E.—KARPUZ, B.: On oscillation of differential and difference equations with non-monotone delays, Appl. Math. Comput. 218 (2011), 3880–3887. Search in Google Scholar

[3] CHATZARAKIS, G.E.: Sufficient oscillation conditions for deviating difference equations, Filomat 33 (2019), no. 11, 3291–3305. Search in Google Scholar

[4] CHATZARAKIS, G. E.—JADLOVSKÁ, I.: Oscillations in deviating difference equations using an iterative technique, J. Inequal. Appl. 2017, Paper No. 173, 24 pp.10.1186/s13660-017-1450-8 Search in Google Scholar

[5] CHATZARAKIS, G.E.—JADLOVSKÁ, I.: Improved iterative oscillation tests for first-order deviating difference equations, Int. J. Difference Equ. 12 (2017), no. 2, 185—210. Search in Google Scholar

[6] CHATZARAKIS, G. E.—KOPLATADZE, R.—STAVROULAKIS, IP.: Oscillation criteria of first order linear difference equations with delay argument, Nonlinear Anal. 68 (2008), 994–1005.10.1016/j.na.2006.11.055 Search in Google Scholar

[7] CHATZARAKIS, G. E.—R. KOPLATADZE, R.—STAVROULAKIS, I. P.: Optimal oscillation criteria for first order difference equations with delay argument, Pacific J. Math. 235 (2008), 15–33.10.2140/pjm.2008.235.15 Search in Google Scholar

[8] CHATZARAKIS, G. E.—PURNARAS, I. K.—STAVROULAKIS, I. P.: Oscillations of deviating difference equations with non-monotone arguments, J. Difference Equ. Appl. 23 (2017), no. 8, 1354–1377. Search in Google Scholar

[9] CHATZARAKIS, G.E.—SHAIKHET, L.: Oscillation criteria for difference equations with non-monotone arguments, Adv. Difference Equ. 2017, Paper No. 62, 16 pp.10.1186/s13662-017-1119-0 Search in Google Scholar

[10] CHATZARAKIS, G. E.—STAVROULAKIS, I. P.: Oscillations of difference equations with general advanced argument, Cent. Eur. J. Math. 10 (2012), 807–823.10.2478/s11533-011-0137-5 Search in Google Scholar

[11] CHEN, M.-P.—YU, J.S.: Oscillations of delay difference equations with variable coefficients. In: Proceedings of the First International Conference on Difference Equations, Gordon and Breach, London, 1994, pp. 105–114. Search in Google Scholar

[12] LI, X.—ZHU, D.: Oscillation of advanced difference equations with variable coefficients, Ann. Differential Equations 18 (2002), 254–263. Search in Google Scholar

[13] TANG, X. H.—YU, J.S.: Oscillation of delay difference equations, Comput. Math. Appl. 37 (1999), 11–20.10.1016/S0898-1221(99)00083-8 Search in Google Scholar

[14] TANG, X. H.— ZHANG, R.Y.: New oscillation criteria for delay difference equations, Comput. Math. Appl. 42 (2001), 1319–1330.10.1016/S0898-1221(01)00243-7 Search in Google Scholar

[15] YAN, W.—MENG, Q.—YAN, J.: Oscillation criteria for difference equation of variable delays, DCDIS Proceedings 3 (2005), 641–647. Search in Google Scholar

[16] ZHANG, B. G. —TIAN, C. J.: Nonexistence and existence of positive solutions for difference equations with unbounded delay, Comput. Math. Appl. 36 (1998), 1–8.10.1016/S0898-1221(98)00103-5 Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo