Home Oscillatory and asymptotic behavior of solutions of third-order quasi-linear neutral difference equations
Article
Licensed
Unlicensed Requires Authentication

Oscillatory and asymptotic behavior of solutions of third-order quasi-linear neutral difference equations

  • T. Gopal , G. Ayyappan , John R. Graef EMAIL logo and E. Thandapani
Published/Copyright: March 28, 2022
Become an author with De Gruyter Brill
Author Information Explore this Subject
Mathematica Slovaca
From the journal Mathematica Slovaca Volume 72 Issue 2

Abstract

By using comparison theorems, the authors investigate the oscillatory and asymptotic behavior of solutions tothe third-order quasi-linear neutral difference equation

Δ a ( n ) Δ 2 z ( n ) α + q ( n ) x β ( σ ( n ) ) = 0 ,

where z(n) = x(n) + px(n − k). Under less restrictive conditions on the coefficient functions and on the delay argument σ(n) than currently found in the literature, their criteria improve a number of known related results. The results are illustrated with examples.

MSC 2010: Primary 39A21
Keywords: Oscillatory behavior; neutral difference equation; quasilinear; third-order; comparison

  1. Communicated by Michal Fečkan

References

[1] Agarwal, R. P.: Difference Equations and Inequalities, Dekker, New York, 2000.10.1201/9781420027020Search in Google Scholar

[2] Agarwal, R. P.—Bohner, M.—Grace, S. R.—O'Regan, D.: Discrete Oscillation Theory, Hindawi, New York, 2005.10.1155/9789775945198Search in Google Scholar

[3] Artzrouni, M.: Generalized stable population theory, J. Math. Biol. 21 (1985), 363–381.10.1007/BF00276233Search in Google Scholar PubMed

[4] Ayyappan, G.: Oscillation criteria of third order nonlinear neutral difference equations, Malaya J. Mat. 3 (2015), 216–223.10.26637/mjm302/013Search in Google Scholar

[5] Jaikumar, S.—Alagesan, K.: Oscillation and asymptotic behavior of third-order difference equations with sub-linear neutral term, J. Sci. Comput. 8 (2019), 34–43.Search in Google Scholar

[6] Jaikumar, S.—Alagesan, K.—Ayyappan, G.: Oscillation of nonlinear third-order delay difference equations with unbounded neutral coefficients, J. Inf. Comput. Sci. 9 (2019), 902–910.Search in Google Scholar

[7] Kocic, V. L.—Ladas, G.: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer, New York, 1993.10.1007/978-94-017-1703-8Search in Google Scholar

[8] Saker, S. H.: Oscillation and asymptotic behavior of third-order nonlinear neutral delay difference equations, Dynam. Systems Appl. 15 (2006), 549–568.Search in Google Scholar

[9] Shoukaku, Y.: On the oscillation of solutions of first-order difference equations with delay, Commun. Math. Anal. 20 (2017), 62–67.Search in Google Scholar

[10] Andruch-Sobilo, A.—Migda, M.: On the oscillation of solutions of third-order linear difference equations of neutral type, Math. Bohemica 130 (2005), 19–33.10.21136/MB.2005.134217Search in Google Scholar

[11] Tang, X. H.—Liu, Y. J.: Oscillation for nonlinear delay difference equations, Tamkang J. Math. 32 (2001), 275–280.10.5556/j.tkjm.32.2001.342Search in Google Scholar

[12] Thandapani, E.—Mahalingam, K.: Oscillatory properties of third-order neutral delay difference equations, Demonstr. Math. 35 (2002), 325–336.10.1515/dema-2002-0213Search in Google Scholar

[13] Thandapani, E.—Selvarangam, S.: Oscillation results for third-order half-linear neutral difference equations, Bull. Math. Anal. Appl. 4 (2012), 91–102.Search in Google Scholar

[14] Thandapani, E.—Selvarangam, S.: Oscillation of third-order half-linear neutral difference equations, Math. Bohemica 138 (2013), 87–104.10.21136/MB.2013.143232Search in Google Scholar

[15] Thandapani, E.—Vijaya, M.—Li, T.: On the oscillation of third order half-linear neutral type difference equations, Electron. J. Qual. Theory Differ. Equ. 2011 (2011), Art No. 76, 1–13.10.14232/ejqtde.2011.1.76Search in Google Scholar

[16] Yildiz, M. K.—Öğünmez, H.: Oscillation results of higher order nonlinear neutral delay difference equations with a nonlinear neutral term, Hacet. J. Math. Stat. 43 (2014), 809–814.Search in Google Scholar
Received: 2020-07-17
Accepted: 2021-02-07
Published Online: 2022-03-28
Published in Print: 2022-04-26

© 2022 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Regular Papers
  2. Logical and algebraic properties of generalized orthomodular posets
  3. Integral prefilters and integral Eq-algebras
  4. Modules with fusion and implication based over distributive lattices: Representation and duality
  5. Localization of k × j-rough Heyting algebras
  6. Meet infinite distributivity for congruence lattices of direct sums of algebras
  7. Some exponential diophantine equations II: The equation x2 – Dy2 = kz for even k
  8. On extensions of the Open Door Lemma
  9. Nevanlinna theory for holomophic curves from annuli into semi-Abelian varieties
  10. Stability and feedback stabilizability of delay periodic differential equations with pairwise permutable matrix functions
  11. On the behaviour solutions of fractional and partial integro differential heat equations and its numerical solutions
  12. Oscillatory and asymptotic behavior of solutions of third-order quasi-linear neutral difference equations
  13. Some properties of Kantorovich variant of Chlodowsky-Szász operators induced by Boas-Buck type polynomials
  14. A Study on statistical versions of convergence of sequences of functions
  15. Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps
  16. Notes on affine Killing and two-Killing vector fields
  17. Prediction of the exponential fractional upper record-values
  18. On concomitants of generalized order statistics from generalized FGM family under a general setting
  19. One-parameter generalization of dual-hyperbolic Pell numbers
https://doi.org/10.1515/ms-2022-0028
Keywords for this article
Oscillatory behavior; neutral difference equation; quasilinear; third-order; comparison

Articles in the same Issue

  1. Regular Papers
  2. Logical and algebraic properties of generalized orthomodular posets
  3. Integral prefilters and integral Eq-algebras
  4. Modules with fusion and implication based over distributive lattices: Representation and duality
  5. Localization of k × j-rough Heyting algebras
  6. Meet infinite distributivity for congruence lattices of direct sums of algebras
  7. Some exponential diophantine equations II: The equation x2 – Dy2 = kz for even k
  8. On extensions of the Open Door Lemma
  9. Nevanlinna theory for holomophic curves from annuli into semi-Abelian varieties
  10. Stability and feedback stabilizability of delay periodic differential equations with pairwise permutable matrix functions
  11. On the behaviour solutions of fractional and partial integro differential heat equations and its numerical solutions
  12. Oscillatory and asymptotic behavior of solutions of third-order quasi-linear neutral difference equations
  13. Some properties of Kantorovich variant of Chlodowsky-Szász operators induced by Boas-Buck type polynomials
  14. A Study on statistical versions of convergence of sequences of functions
  15. Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps
  16. Notes on affine Killing and two-Killing vector fields
  17. Prediction of the exponential fractional upper record-values
  18. On concomitants of generalized order statistics from generalized FGM family under a general setting
  19. One-parameter generalization of dual-hyperbolic Pell numbers
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 27.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2022-0028/html
Scroll to top button