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Periodic solutions of nonlinear vector difference equations

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.

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References

  1. 1.

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

  2. 2.

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

  3. 3.

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

  4. 4.

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

  5. 5.

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

  6. 6.

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

  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

  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.

  9. 9.

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

  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.

  11. 11.

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

  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

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Correspondence to MI Gil'.

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

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Keywords

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