Skip to main content
SpringerLink
Log in

On Positive Solutions of Nonlinear Third-Order Impulsive Boundary Value Problems on Time Scales

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this paper, using four functionals fixed point theorem, we obtain sufficient conditions for the existence of at least one positive solution of a third-order impulsive boundary value problem with integral boundary conditions on time scales. As an application, we give two examples to demonstrate our main result.

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. Akhmet, M.: Principles of Discontinuous Dynamical Systems. Springer, New York (2010)

  2. Avery R., Henderson J., O’Regan D.: Four functionals fixed point theorem. Math. Comput. Model. 48, 1081–1089 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Benchohra, M., Henderson, J., Ntouyas, S.: Impulsive Differential Equations and Inclusions. Hindawi Publishing Corporation, New York (2006)

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

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

  6. Boucherif A.: Second-order boundary value problems with integral boundary conditions. Nonlinear Anal. 70, 364–371 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cui X.Y., Shi X.Y.: Existence of solutions for first-order impulsive dynamic equations on time scales with integral boundary conditions. Math. Pract. Theory 42, 193–198 (2012)

    MathSciNet  Google Scholar 

  8. Fen, F.T., Karaca, I.Y.: Existence of positive solutions for nonlinear second-order impulsive boundary value problems on time scales. Mediterr. J. Math. 13, 191–204 (2016). doi:10.1007/s00009-014-0494-y

  9. Feng M., Du B., Ge W.: Impulsive boundary value problems with integral boundary conditions and one-dimensional p-Laplacian. Nonlinear Anal. 70, 3119–3126 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Graef J.R., Ouahab A.: Some existence results for impulsive dynamic equations on time scales with integral boundary conditions. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 13B, 11–24 (2006)

    MathSciNet  Google Scholar 

  11. Hilger, S.: Ein Masskettenkalkül mit Anwendug auf Zentrumsmanningfaltigkeiten. Ph.D. Thesis, Universitat Würzburg (1988)

  12. Hu L., Liu L., Wu Y.: Positive solutions of nonlinear singular two-point boundary value problems for second-order impulsive differential equations. Appl. Math. Comput. 196, 550–562 (2008)

    MathSciNet  MATH  Google Scholar 

  13. Hu M., Wang L.: Triple positive solutions for an impulsive dynamic equation with integral boundary condition on time scales. Int. J. Appl. Math. Stat. 31, 67–78 (2013)

    MathSciNet  Google Scholar 

  14. Karaca I.Y., Fen F.T.: Positive solutions of nth-order boundary value problems with integral boundary conditions. Math. Model. Anal. 20(2), 188–204 (2015)

    Article  MathSciNet  Google Scholar 

  15. Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)

  16. Li, Y., Shu, J.: Multiple positive solutions for first-order impulsive integral boundary value problems on time scales. Bound. Value Probl. 2011:12, 19 (2011)

  17. Lv Z.W., Liang J., Xiao T.J.: Multiple positive solutions for second order impulsive boundary value problems in Banach spaces. Electron. J. Qual Theory Differ. Equ. 38, 1–15 (2010)

    MathSciNet  MATH  Google Scholar 

  18. Samoilenko, A.M., Perestyuk, N.A.: Impulsive Differential Equations. World Scientific, Singapore (1995)

  19. Zhang X., Feng M., Ge W.: Existence results for nonlinear boundary-value problems with integral boundary conditions in Banach spaces. Nonlinear Anal. 69, 3310–3321 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Ege University, 35100, Bornova, Izmir, Turkey

    Ilkay Yaslan Karaca

  2. Department of Mathematics, Gazi University, 06500, Teknikokullar, Ankara, Turkey

    Fatma Tokmak Fen

Authors
  1. Ilkay Yaslan Karaca
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fatma Tokmak Fen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fatma Tokmak Fen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karaca, I.Y., Fen, F.T. On Positive Solutions of Nonlinear Third-Order Impulsive Boundary Value Problems on Time Scales. Mediterr. J. Math. 13, 4447–4461 (2016). https://doi.org/10.1007/s00009-016-0755-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00009-016-0755-z

Mathematics Subject Classification

Keywords

Search

Navigation