Skip to main content

Oscillatory mixed difference systems

Abstract

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.

[12345678910111234567891011]

References

  1. 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)00115-6

    MathSciNet  Article  MATH  Google Scholar 

  2. 2.

    Agarwal RP, Grace SR, O'Regan D: Oscillation Theory for Difference and Functional Differential Equations. Kluwer Academic, Dordrecht; 2000:viii+337.

    Book  MATH  Google Scholar 

  3. 3.

    Chuanxi Q, Kuruklis SA, Ladas G: Oscillations of linear autonomous systems of difference equations. Applicable Analysis 1990,36(1–2):51–63. 10.1080/00036819008839921

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Coppel WA: Stability and Asymptotic Behavior of Differential Equations. D. C. Heath, Massachusetts; 1965:viii+166.

    MATH  Google Scholar 

  5. 5.

    Desoer CA, Vidyasagar M: Feedback Systems: Input-Output Properties. Academic Press, New York; 1975:xvi+266.

    MATH  Google Scholar 

  6. 6.

    Ferreira JM, Pedro AM: Oscillations of delay difference systems. Journal of Mathematical Analysis and Applications 1998,221(1):364–383. 10.1006/jmaa.1997.5905

    MathSciNet  Article  MATH  Google Scholar 

  7. 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)00421-9

    MathSciNet  Article  MATH  Google Scholar 

  8. 8.

    Györi I, Ladas G: Oscillation Theory of Delay Differential Equations, Oxford Mathematical Monographs. Oxford University Press, New York; 1991:xii+368.

    MATH  Google Scholar 

  9. 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. 10.1137/0522046

    MathSciNet  Article  MATH  Google Scholar 

  10. 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.

    MathSciNet  MATH  Google Scholar 

  11. 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.2000.6735

    MathSciNet  Article  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to JoséM Ferreira.

Rights and permissions

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

Reprints and Permissions

About this article

Cite this article

Ferreira, J., Pinelas, S. Oscillatory mixed difference systems. Adv Differ Equ 2006, 092923 (2006). https://doi.org/10.1155/ADE/2006/92923

Download citation

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation