Nonlinear Oscillations

, Volume 11, Issue 4, pp 527–538 | Cite as

On positive periodic solutions of nonlinear impulsive functional differential equations

  • O. I. Kocherha
  • O. I. Nenya
  • V. I. Tkachenko
Article

Using the Krasnosel’skii theorem on a fixed point of a mapping in a cone, we obtain conditions for the existence of positive, piecewise-smooth, periodic solutions of impulsive functional differential equations.

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References

  1. 1.
    D. Franco, E. Liz, and P. J. Torres, “Existence of periodic solutions for functional equations with periodic delay,” Indian J. Pure Appl. Math., 38, 143–152 (2007).MATHMathSciNetGoogle Scholar
  2. 2.
    D. Jiang, J. Wei, and B. Zhang, “Positive periodic solutions of functional differential equations and population models,” Electron. J. Different. Equat., No. 71, 1–13 (2002).Google Scholar
  3. 3.
    Y. Li and L. Zhu, “Positive periodic solutions of nonlinear functional differential equations,” Appl. Math. Comput., 156, 329–339 (2004).MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    H. Wang, “Positive periodic solutions of functional differential equations,” J. Different. Equat., 202, 354–366 (2004).MATHCrossRefGoogle Scholar
  5. 5.
    W. Zhang, D. Zhu, and P. Bi, “Existence of periodic solutions of a scalar functional differential equation via fixed point theorem,” Math. Comput. Modelling, 46, 718–729 (2007).MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    N. Zhang, B. Dai, and X. Qian, “Periodic solutions for a class of higher-dimension functional differential equations with impulses,” Nonlin. Analysis, 68, 629–638 (2008).MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    X. Zhang, D. Jiang, X. Li, and K. Wang, “A new existence theory for single and multiple positive periodic solutions to Volterra integro-differential equations with impulsive effects,” Comput. Math. Appl., 51, 17–32 (2006).MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    X. Zhang, J. Yan, and A. Zhao, “Existence of positive periodic solutions for an impulsive differential equation,” Nonlin. Analysis, 68, 3209–3216 (2008).MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore (1995).MATHGoogle Scholar
  10. 10.
    K. Deimling, Nonlinear Functional Analysis, Springer, Berlin (1985).MATHGoogle Scholar
  11. 11.
    M. A. Krasnoselskii, Positive Solutions of Operator Equations, Noordhoff, Groningen (1964).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • O. I. Kocherha
    • 1
  • O. I. Nenya
    • 2
  • V. I. Tkachenko
    • 3
  1. 1.Nizhyn UniversityNizhynUkraine
  2. 2.Kyiv National Economic UniversityKyivUkraine
  3. 3.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine

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