Skip to main content
SpringerLink
Log in

Existence of positive solutions of delay dynamic equations

  • Published:
Positivity Aims and scope Submit manuscript

Abstract

In this article we study the existence of positive solutions for a dynamic equations on time scales. The main tool employed here is the Schauder’s fixed point theorem. The asymptotic properties of solutions are also treated. The results obtained here extend the work of Dorociakova and Olach (Tatra Mt Math Publ 43:63–70, 2009). Three examples are also given to illustrate this work.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Adivar, M., Raffoul, Y.N.: Existence of periodic solutions in totally nonlinear delay dynamic equations. Electron. J. Qual. Theory Differ. Equ. 1, 1–20 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ardjouni, A., Djoudi, A.: Existence of positive periodic solutions for nonlinear neutral dynamic equations with variable delay on a time scale. Malaya J. Mat. 2(1), 60–67 (2013)

    MATH  Google Scholar 

  3. Ardjouni, A., Djoudi, A.: Existence of periodic solutions for nonlinear neutral dynamic equations with functional delay on a time scale. Acta Univ. Palacki. Olomuc. Fac. Rerum Nat. Math. 52(1), 5–19 (2013)

    MathSciNet  MATH  Google Scholar 

  4. Ardjouni, A., Djoudi, A.: Existence of periodic solutions for nonlinear neutral dynamic equations with variable delay on a time scale. Commun. Nonlinear Sci. Numer. Simul. 17, 3061–3069 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ardjouni, A., Djoudi, A.: Periodic solutions in totally nonlinear dynamic equations with functional delay on a time scale. Rend. Sem. Mat. Univ. Politec. Torino 68(4), 349–359 (2010)

    MathSciNet  MATH  Google Scholar 

  6. Bohner, M., Peterson, A.: Dynamic Equations on Time Scales, An Introduction with Applications. Birkhäuser, Boston (2001)

    Book  MATH  Google Scholar 

  7. Bohner, M., Peterson, A.: Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston (2003)

    Book  MATH  Google Scholar 

  8. Dorociakova, B., Olach, R.: Existence of positive solutions of delay differential equations. Tatra Mt. Math. Publ. 43, 63–70 (2009)

    MathSciNet  MATH  Google Scholar 

  9. Hilger, S.: Ein Masskettenkalkül mit Anwendung auf Zentrumsmanningfaltigkeiten. PhD thesis, Universität Würzburg, (1988)

  10. Kaufmann, E.R., Raffoul, Y.N.: Periodic solutions for a neutral nonlinear dynamical equation on a time scale. J. Math. Anal. Appl. 319, 315–325 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kaufmann, E.R., Raffoul, Y.N.: Periodicity and stability in neutral nonlinear dynamic equation with functional delay on a time scale. Electron. J. Differ. Equ. 2007(27), 1–12 (2007)

    MathSciNet  MATH  Google Scholar 

  12. Lakshmikantham, V., Sivasundaram, S., Kaymarkcalan, B.: Dynamic Systems on Measure Chains. Kluwer Academic Publishers, Dordrecht (1996)

    Book  Google Scholar 

  13. Olach, R.: Positive periodic solutions of delay differential equations. Appl. Math. Lett. 26, 1141–1145 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  14. Smart, D.R.: Fixed Points Theorems. Cambridge University Press, Cambridge (1980)

    MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous referee for his/her valuable comments and good advice.

Author information

Authors and Affiliations

  1. Faculty of Sciences, Department of Mathematics, Univ Annaba, P.O. Box 12, 23000, Annaba, Algeria

    Faycal Bouchelaghem

  2. Department of Mathematics and Informatics, Univ Souk Ahras, P.O. Box 1553, 41000, Souk Ahras, Algeria

    Abdelouaheb Ardjouni

  3. Applied Mathematics Lab., Faculty of Sciences, Department of Mathematics, Univ Annaba, P.O. Box 12, 23000, Annaba, Algeria

    Abdelouaheb Ardjouni & Ahcene Djoudi

Authors
  1. Faycal Bouchelaghem
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdelouaheb Ardjouni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ahcene Djoudi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdelouaheb Ardjouni.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bouchelaghem, F., Ardjouni, A. & Djoudi, A. Existence of positive solutions of delay dynamic equations. Positivity 21, 1483–1493 (2017). https://doi.org/10.1007/s11117-017-0480-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11117-017-0480-2

Keywords

Mathematics Subject Classification

Search

Navigation