Open Access

On third-order linear difference equations involving quasi-differences

Advances in Difference Equations20062006:065652

https://doi.org/10.1155/ADE/2006/65652

Received: 30 June 2004

Accepted: 12 October 2004

Published: 24 January 2006

Abstract

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.

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Authors’ Affiliations

(1)
Department of Mathematics, Masaryk University

References

  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/BF01783478View ArticleMathSciNetMATHGoogle 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.MathSciNetView ArticleMATHGoogle 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.Google Scholar
  5. Elias U: Oscillation Theory of Two-Term Differential Equations, Mathematics and Its Applications. Volume 396. Kluwer Academic, Dordrecht; 1997:viii+217.View ArticleGoogle 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.MathSciNetMATHGoogle 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-1987-17-3-597MathSciNetView ArticleMATHGoogle Scholar
  9. Smith B: Oscillation and nonoscillation theorems for third order quasi-adjoint difference equations. Portugaliae Mathematica 1988,45(3):229–243.MathSciNetMATHGoogle 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/1181072673MathSciNetView ArticleMATHGoogle 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.MathSciNetMATHGoogle Scholar

Copyright

© Došlá and Kobza 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.