Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


IMPACT FACTOR 2018: 0.490

CiteScore 2018: 0.47

SCImago Journal Rank (SJR) 2018: 0.279
Source Normalized Impact per Paper (SNIP) 2018: 0.627

Mathematical Citation Quotient (MCQ) 2017: 0.26

Online
ISSN
1337-2211
See all formats and pricing
More options …
Volume 68, Issue 5

Issues

Oscillation tests for difference equations with several non-monotone deviating arguments

George E. Chatzarakis
  • Department of Electrical and Electronic Engineering Educators School of Pedagogical and Technological Education (ASPETE) 14121, N. Heraklio Athens GREECE
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Lana Horvat Dmitrović / Mervan Pašić
Published Online: 2018-10-20 | DOI: https://doi.org/10.1515/ms-2017-0170

Abstract

The purpose of this paper is to derive sufficient conditions for the oscillation of all solutions of a difference equation with several non-monotone deviating arguments and nonnegative coefficients. Corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the significance of the results are also given.

MSC 2010: 39A10; 39A21

Keywords: difference equation; non-monotone arguments; oscillatory solutions; nonoscillatory solutions; Gronwall inequality

References

  • [1]

    BAINOV, D.—SIMEONOV, P.:Integral Inequalities and Applications, Kluwer Academic Publisher, 1992.Google Scholar

  • [2]

    BEREZANSKY, L.—BRAVERMAN, E.:On existence of positive solutions for linear difference equations with several delays,Adv. Dyn. Syst. Appl. 1 (2006), 29–47.Google Scholar

  • [3]

    BRAVERMAN, E.—CHATZARAKIS, G. E.—STAVROULAKIS, I. P.:Iterative oscillation tests for difference equations with severalnon-monotone arguments, J. Difference Equ. Appl. 2015, 21 pp.,http://dx.doi.org/10.1080/10236198.2015.1051480.Google Scholar

  • [4]

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

  • [5]

    CHATZARAKIS, G. E.—KUSANO T.—STAVROULAKIS, I. P.:Oscillation conditions for difference equations with several variablearguments, Math. Bohem. 140(3) (2015), 291–311.Google Scholar

  • [6]

    CHATZARAKIS, G. E.—MANOJLOVIC, J.—PINELAS, S.—STAVROULAKIS, I. P.:Oscillation criteria of difference equations with several deviating arguments,Yokohama Math. J. 60 (2014), 13–31.Google Scholar

  • [7]

    CHATZARAKIS, G. E.—PINELAS, S.—STAVROULAKIS, I. P.:Oscillations of difference equations with several deviated arguments,Aequationes Math. 88 (2014), 105–123.Web of ScienceCrossrefGoogle Scholar

  • [8]

    ELAYDI, S. N.:An Introduction to Difference Equations,3rd Edition, Springer, New York, 2005.Google Scholar

  • [9]

    ERBE, L. H.—KONG, Q. K.—ZHANG, B. G.:Oscillation Theory for Functional Differential Equations,Marcel Dekker, New York, 1995.Google Scholar

  • [10]

    LI, X.—ZHU, D.: Oscillation of advanced differenceequations with variable coefficients, Ann. DifferentialEquations 18 (2002), 254–263.Google Scholar

  • [11]

    LUO, X. N.—ZHOU, Y.—LI, C. F.:Oscillations of a nonlinear difference equation with several delays,Math. Bohem. 128 (2003), 309–317.Google Scholar

  • [12]

    STAVROULAKIS, I. P.:Oscillation criteria for delay and difference equations with non-monotone arguments,Adv. Appl. Math. 226 (2014), 661–672.Google Scholar

  • [13]

    TANG, X. H.—YU, J. S.:Oscillation of delay difference equations,Comput. Math. Appl. 37 (1999), 11–20.CrossrefGoogle Scholar

  • [14]

    TANG X. H.—ZHANG, R. Y.: New oscillation criteriafor delay difference equations, Comput. Math. Appl. 42(2001), 1319–1330.CrossrefGoogle Scholar

  • [15]

    WANG, X.:Oscillation of delay difference equations with several delays,J. Math. Anal. Appl. 286 (2003), 664–674.CrossrefGoogle Scholar

  • [16]

    YAN, W.—MENG, Q.—YAN, J.: Oscillation criteria fordifference equation of variable delays, DCDIS Proceedings 3(2005), 641–647.Google Scholar

  • [17]

    ZHANG B. G.—TIAN, C. J.:Nonexistence and existenceof positive solutions for difference equations with unbounded delay,Comput. Math. Appl. 36 (1998), 1–8.CrossrefGoogle Scholar

  • [18]

    ZHANG, B. G.—ZHOU, Y.:Oscillations of differenceequations with several delays, Comput. Math. Appl. 44(2002), 817–821.CrossrefGoogle Scholar

About the article

E-mail: gea.xatz@aspete.gr


Received: 2017-02-14

Accepted: 2017-10-10

Published Online: 2018-10-20

Published in Print: 2018-10-25


Communicated by Michal Fečkan


Citation Information: Mathematica Slovaca, Volume 68, Issue 5, Pages 1083–1096, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0170.

Export Citation

© 2018 Mathematical Institute Slovak Academy of Sciences.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
George E. Chatzarakis and Mervan Pašić
Journal of Difference Equations and Applications, 2018, Page 1

Comments (0)

Please log in or register to comment.
Log in