Skip to main content
Advances in Difference Equations
Advances in Difference Equations Cover Image
Download PDF

Periodic solutions of nonlinear vector difference equations

Advances in Difference Equations volume 2006, Article number: 039419 (2006) Cite this article

Abstract

Essentially nonlinear difference equations in a Euclidean space are considered. Conditions for the existence of periodic solutions and solution estimates are derived. Our main tool is a combined usage of the recent estimates for matrix-valued functions with the method of majorants.

[123456789101112]

References

  1. 1.

    Cheng SS, Zhang G: Positive periodic solutions of a discrete population model. Functional Differential Equations 2000,7(3–4):223–230.

    MathSciNet  MATH  Google Scholar 

  2. 2.

    Elaydi S, Zhang S: Stability and periodicity of difference equations with finite delay. Funkcialaj Ekvacioj. Serio Internacia 1994,37(3):401–413.

    MathSciNet  MATH  Google Scholar 

  3. 3.

    Gil' MI: Periodic solutions of abstract difference equations. Applied Mathematics E-Notes 2001, 1: 18–23.

    MathSciNet  MATH  Google Scholar 

  4. 4.

    Gil' MI: Operator Functions and Localization of Spectra, Lecture Notes in Mathematics. Volume 1830. Springer, Berlin; 2003:xiv+256.

    Google Scholar 

  5. 5.

    Gil' MI, Cheng SS: Periodic solutions of a perturbed difference equation. Applicable Analysis 2000,76(3–4):241–248.

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Gil' MI, Kang S, Zhang G: Positive periodic solutions of abstract difference equations. Applied Mathematics E-Notes 2004, 4: 54–58.

    MathSciNet  MATH  Google Scholar 

  7. 7.

    Halanay A: Solutions périodiques et presque-périodiques des systèmes d'équations aux différences finies. Archive for Rational Mechanics and Analysis 1963, 12: 134–149. 10.1007/BF00281222

    MathSciNet  Article  MATH  Google Scholar 

  8. 8.

    Halanay A, Rǎsvan V: Stability and Stable Oscillations in Discrete Time Systems, Advances in Discrete Mathematics and Applications. Volume 2. Gordon and Breach Science, Amsterdam; 2000.

    Google Scholar 

  9. 9.

    Pelyukh GP: On the existence of periodic solutions of discrete difference equations. Uzbekskiĭ Matematicheskiĭ Zhurnal 1995, (3):88–90.

    Google Scholar 

  10. 10.

    Turaev Kh: On the existence and uniqueness of periodic solutions of a class of nonlinear difference equations. Uzbekskiĭ Matematicheskiĭ Zhurnal 1994, (2):52–54.

    Google Scholar 

  11. 11.

    Zeidler E: Nonlinear Functional Analysis and Its Applications. I. Fixed-point Theorems. Springer, New York; 1986:xxi+897.

    Google Scholar 

  12. 12.

    Zhang RY, Wang ZC, Chen Y, Wu J: Periodic solutions of a single species discrete population model with periodic harvest/stock. Computers & Mathematics with Applications 2000,39(1–2):77–90. 10.1016/S0898-1221(99)00315-6

    MathSciNet  Article  MATH  Google Scholar 

Download references

Author information

Affiliations

  1. Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva, 84105, Israel

    MI Gil'

Authors
  1. MI Gil'
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to MI Gil'.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Gil', M. Periodic solutions of nonlinear vector difference equations. Adv Differ Equ 2006, 039419 (2006). https://doi.org/10.1155/ADE/2006/39419

Download citation

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Periodic Solution