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On third-order linear difference equations involving quasi-differences


We study the third-order linear difference equation with quasi-differences and its adjoint equation. The main results of the paper describe relationships between the oscillatory and nonoscillatory solutions of both equations.



  1. Agarwal RP: Difference Equations and Inequalities, Monographs and Textbooks in Pure and Applied Mathematics. Volume 228. 2nd edition. Marcel Dekker, New York; 2000:xvi+971.

    Google Scholar 

  2. Cecchi M, Došlá Z, Marini M: An equivalence theorem on properties A, B for third order differential equations. Annali di Matematica Pura ed Applicata. Series IV 1997, 173: 373–389. 10.1007/BF01783478

    Article  MathSciNet  MATH  Google Scholar 

  3. Došlá Z, Kobza A: Global asymptotic properties of third-order difference equations. Computers & Mathematics with Applications. An International Journal 2004,48(1–2):191–200.

    Article  MathSciNet  MATH  Google Scholar 

  4. Došlá Z, Kobza A: On nonoscillatory solutions of third order difference equations. In Proceedings of the Eighth International Conference of Difference Equations and Applications, 2005, Boca Raton, Fla. Edited by: Elaydi S, Ladas G, Aulbach B, Dosly O. Taylor & Francis, Chapman & Hall/CRC; 105–112.

  5. Elias U: Oscillation Theory of Two-Term Differential Equations, Mathematics and Its Applications. Volume 396. Kluwer Academic, Dordrecht; 1997:viii+217.

    Book  Google Scholar 

  6. Migda M: Nonoscillatory solutions of some higher order difference equations. In Colloquium on Differential and Difference Equations, CDDE 2002 (Brno), Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math.. Volume 13. Masaryk University, Brno; 2003:177–184.

    Google Scholar 

  7. Popenda J, Schmeidel E: Nonoscillatory solutions of third order difference equations. Portugaliae Mathematica 1992,49(2):233–239.

    MathSciNet  MATH  Google Scholar 

  8. Smith B: Oscillatory and asymptotic behavior in certain third order difference equations. The Rocky Mountain Journal of Mathematics 1987,17(3):597–606. 10.1216/RMJ-1987-17-3-597

    Article  MathSciNet  MATH  Google Scholar 

  9. Smith B: Oscillation and nonoscillation theorems for third order quasi-adjoint difference equations. Portugaliae Mathematica 1988,45(3):229–243.

    MathSciNet  MATH  Google Scholar 

  10. Smith B: Linear third-order difference equations: oscillatory and asymptotic behavior. The Rocky Mountain Journal of Mathematics 1992,22(4):1559–1564. 10.1216/rmjm/1181072673

    Article  MathSciNet  MATH  Google Scholar 

  11. Wong PJY, Agarwal RP: Nonoscillatory solutions of functional difference equations involving quasi-differences. Fako de l'Funkcialaj Ekvacioj Japana Matematika Societo. Funkcialaj Ekvacioj. Serio Internacia 1999,42(3):389–412.

    MathSciNet  MATH  Google Scholar 

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Correspondence to Zuzana Došlá.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Došlá, Z., Kobza, A. On third-order linear difference equations involving quasi-differences. Adv Differ Equ 2006, 065652 (2006).

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