Skip to main content
Log in

Even Number of Positive Solutions for the System of (pq)-Laplacian Fractional Order Two-Point Boundary Value Problems

  • Original Research
  • Published:
Differential Equations and Dynamical Systems Aims and scope Submit manuscript

Abstract

In this paper, we derive sufficient conditions for the existence of at least two positive solutions for a system of (pq)-Laplacian fractional order two-point boundary value problems by using an Avery–Henderson functional fixed point theorem. We also establish the existence of at least 2m positive solutions to the boundary value problem for an arbitrary positive integer m.

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

Access this article

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. Agarwal, R.P., O’Regan, D., Wong, P.J.Y.: Positive solutions of differential, difference and integral equations. Kluwer Academic Publishers, Dordrecht (1999)

    Book  Google Scholar 

  2. Anderson, D.R., Davis, J.M.: Multiple positive solutions and eigenvalues for third order right focal boundary value problems. J. Math. Anal. Appl. 267, 135–157 (2002)

    Article  MathSciNet  Google Scholar 

  3. Avery, R.I., Henderson, J.: Two positive fixed points of nonlinear operators on ordered Banach spaces. Comm. Appl. Nonlinear Anal. 8, 27–36 (2001)

    MathSciNet  MATH  Google Scholar 

  4. Avery, R.I., Henderson, J.: Existence of three positive pseudo-symmetric solutions for a one-dimensional \(p\)-Laplacian. J. Math. Anal. Appl. 277, 395–404 (2003)

    Article  MathSciNet  Google Scholar 

  5. Bai, C.: Existence of positive solutions for boundary value problems of fractional functional differential equations. Elec. J. Qual. Theory Diff. Equ. 30, 1–14 (2010)

    MathSciNet  Google Scholar 

  6. Chai, G.: Positive solutions for boundary value problem of fractional differential equation with \(p\)-Laplacian operator. Bound. Value Probl. 2012, 1–18 (2012)

    Article  MathSciNet  Google Scholar 

  7. Chen, T., Liu, W.: An anti-periodic boundary value problem for the fractional differential equation with a \(p\)-Laplacian operator. Appl. Math. Lett. 25, 1671–1675 (2012)

    Article  MathSciNet  Google Scholar 

  8. Diening, L., Lindqvist, P., Kawohl, B.: Mini-Workshop: the \(p\)-Laplacian operator and applications. Oberwolfach Rep. 10, 433–482 (2013)

    Article  MathSciNet  Google Scholar 

  9. Erbe, L.H., Wang, H.: On the existence of positive solutions of ordinary differential equations. Proc. Am. Math. Soc. 120, 743–748 (1994)

    Article  MathSciNet  Google Scholar 

  10. Goodrich, C.: Existence of a positive solution to systems of differential equations of fractional order. Comput. Math. Appl. 62, 1251–1268 (2011)

    Article  MathSciNet  Google Scholar 

  11. Guo, D., Lakshmikantham, V.: Nonlinear problems in abstract cones. Acadamic Press, San Diego (1988)

    MATH  Google Scholar 

  12. Henderson, J., Ntouyas, S.K.: Positive solutions for systems of nonlinear boundary value problems. Nonlinear Stud. 15, 51–60 (2008)

    MathSciNet  MATH  Google Scholar 

  13. Kilbas, A.A., Srivasthava, H.M., Trujillo, J.J.: Theory and applications of fractional differential equations, North-Holland mathematics studies, vol. 204. Elsevier Science, Amsterdam (2006)

    Google Scholar 

  14. Kong, L., Wang, J.: Multiple positive solutions for the one-dimensional \(p\)-Laplacian. Nonlinear Anal. 42, 1327–1333 (2000)

    Article  MathSciNet  Google Scholar 

  15. Podulbny, I.: Fractional diffrential equations. Academic Press, San Diego (1999)

    Google Scholar 

  16. Prasad, K.R., Krushna, B.M.B.: Multiple positive solutions for a coupled system of Riemann-Liouville fractional order two-point boundary value problems. Nonlinear Stud. 20, 501–511 (2013)

    MathSciNet  MATH  Google Scholar 

  17. Prasad, K.R., Krushna, B.M.B.: Multiple positive solutions for a coupled system of \(p\)-Laplacian fractional order two-point boundary value problems. Int. J. Differ. Equ., 1–10 (2014) (article ID 485647)

  18. Yang, C., Yan, J.: Positive solutions for third order Sturm-Liouville boundary value problems with \(p\)-Laplacian. Comput. Math. Appl. 59, 2059–2066 (2010)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors thank the referees for their valuable suggestions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to K. R. Prasad.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Prasad, K.R., Krushna, B.M.B. & Sreedhar, N. Even Number of Positive Solutions for the System of (pq)-Laplacian Fractional Order Two-Point Boundary Value Problems. Differ Equ Dyn Syst 26, 315–330 (2018). https://doi.org/10.1007/s12591-016-0281-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12591-016-0281-2

Keywords

Mathematics Subject Classification

Navigation