Open Access

Oscillatory mixed difference systems

Advances in Difference Equations20062006:092923

DOI: 10.1155/ADE/2006/92923

Received: 2 November 2005

Accepted: 21 February 2006

Published: 8 June 2006


The aim of this paper is to discuss the oscillatory behavior of difference systems of mixed type. Several criteria for oscillations are obtained. Particular results are included in regard to scalar equations.


Authors’ Affiliations

Departamento de Matemática, Instituto Superior Técnico
Departamento de Matemática, Universidade dos Açores


  1. Agarwal RP, Grace SR: The oscillation of certain difference equations. Mathematical and Computer Modelling 1999,30(1–2):53–66. 10.1016/S0895-7177(99)00115-6MathSciNetView ArticleMATHGoogle Scholar
  2. Agarwal RP, Grace SR, O'Regan D: Oscillation Theory for Difference and Functional Differential Equations. Kluwer Academic, Dordrecht; 2000:viii+337.View ArticleMATHGoogle Scholar
  3. Chuanxi Q, Kuruklis SA, Ladas G: Oscillations of linear autonomous systems of difference equations. Applicable Analysis 1990,36(1–2):51–63. 10.1080/00036819008839921MathSciNetView ArticleMATHGoogle Scholar
  4. Coppel WA: Stability and Asymptotic Behavior of Differential Equations. D. C. Heath, Massachusetts; 1965:viii+166.MATHGoogle Scholar
  5. Desoer CA, Vidyasagar M: Feedback Systems: Input-Output Properties. Academic Press, New York; 1975:xvi+266.MATHGoogle Scholar
  6. Ferreira JM, Pedro AM: Oscillations of delay difference systems. Journal of Mathematical Analysis and Applications 1998,221(1):364–383. 10.1006/jmaa.1997.5905MathSciNetView ArticleMATHGoogle Scholar
  7. Ferreira JM, Pinelas S: Oscillatory retarded functional systems. Journal of Mathematical Analysis and Applications 2003,285(2):506–527. 10.1016/S0022-247X(03)00421-9MathSciNetView ArticleMATHGoogle Scholar
  8. Györi I, Ladas G: Oscillation Theory of Delay Differential Equations, Oxford Mathematical Monographs. Oxford University Press, New York; 1991:xii+368.MATHGoogle Scholar
  9. Györi I, Ladas G, Pakula L: Conditions for oscillation of difference equations with applications to equations with piecewise constant arguments. SIAM Journal on Mathematical Analysis 1991,22(3):769–773. 10.1137/0522046MathSciNetView ArticleMATHGoogle Scholar
  10. Kirchner J, Stroinski U: Explicit oscillation criteria for systems of neutral differential equations with distributed delay. Differential Equations and Dynamical Systems 1995,3(1):101–120.MathSciNetMATHGoogle Scholar
  11. Krisztin T: Nonoscillation for functional differential equations of mixed type. Journal of Mathematical Analysis and Applications 2000,245(2):326–345. 10.1006/jmaa.2000.6735MathSciNetView ArticleMATHGoogle Scholar


© J. M. Ferreira and S. Pinelas 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.