Skip to main content
SpringerLink
Log in

On a first-order semipositone discrete fractional boundary value problem

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

Abstract

In this paper we demonstrate the existence of at least one positive solution to a discrete fractional semipositone boundary value problem. Our results extend existing results not only due to the fact that the problem we treat here is of fractional order but also due to the fact that the boundary condition we study is potentially very general being as it can be both nonlocal and nonlinear.

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. R. Agarwal, M. Meehan, and D. O’Regan, Fixed Point Theory and Applications, Cambridge University Press, 2001.

  2. Anderson D.R.: Existence of solutions for first-order multi-point problems with changing-sign nonlinearity, J. Difference Equ. Appl. 14, 657–666 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Anderson D.R., Zhai C.: Positive solutions to semi-positone second-order three-point problems on time scales, Appl. Math. Comput. 215, 3713–3720 (2010)

    MathSciNet  MATH  Google Scholar 

  4. Atici F.M., Eloe P.W.: Initial value problems in discrete fractional calculus, Proc. Amer. Math. Soc. 137, 981–989 (2009)

    MathSciNet  MATH  Google Scholar 

  5. Atici F.M., Eloe P.W.: Two-point boundary value problems for finite fractional difference equations, J. Difference Equ. Appl. 17, 445–456 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Atici F.M., Şengül S.: Modeling with fractional difference equations, J. Math. Anal. Appl. 369, 1–9 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  8. Feng M.: Existence of symmetric positive solutions for a boundary value problem with integral boundary conditions, Appl. Math. Lett. 24, 1419–1427 (2011)

    Article  MATH  Google Scholar 

  9. Ferreira R.A.C.: A discrete fractional Gronwall inequality, Proc. Amer. Math. Soc. 140, 1605–1612 (2012)

    Article  MATH  Google Scholar 

  10. Goodrich C.S.: Solutions to a discrete right-focal boundary value problem, Int. J. Difference Equ. 5, 195–216 (2010)

    MathSciNet  Google Scholar 

  11. Goodrich C.S.: Continuity of solutions to discrete fractional initial value problems, Comput. Math. Appl. 59, 3489–3499 (2010)

    MathSciNet  MATH  Google Scholar 

  12. Goodrich C.S.: On discrete sequential fractional boundary value problems, J. Math. Anal. Appl. 385, 111–124 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Goodrich C.S.: Positive solutions to boundary value problems with nonlinear boundary conditions, Nonlinear Anal. 75, 417–432 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Goodrich C.S.: On a discrete fractional three-point boundary value problem, J. Difference Equ. Appl. 18, 397–415 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Goodrich C.S.: Nonlocal systems of BVPs with asymptotically superlinear boundary conditions, Comment. Math. Univ. Carolin. 53, 79–97 (2012)

    MathSciNet  MATH  Google Scholar 

  16. Goodrich C.S.: On nonlocal BVPs with boundary conditions with asymptotically sublinear or superlinear growth, Math. Nachr. 285, 1404–1421 (2012)

    MathSciNet  MATH  Google Scholar 

  17. Goodrich C.S.: On nonlinear boundary conditions satisfying certain asymptotic behavior, Nonlinear Anal. 76, 58–67 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  18. Holm M.: Sum and difference compositions and applications in discrete fractional calculus. Cubo 13, 153–184 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Infante G.: Nonlocal boundary value problems with two nonlinear boundary conditions, Commun. Appl. Anal. 12, 279–288 (2008)

    MathSciNet  MATH  Google Scholar 

  20. Infante G., Pietramala P.: A third order boundary value problem subject to nonlinear boundary conditions, Math. Bohem. 135, 113–121 (2010)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Creighton Preparatory School, Omaha, NE, 68114, USA

    Christopher S. Goodrich

Authors
  1. Christopher S. Goodrich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christopher S. Goodrich.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goodrich, C.S. On a first-order semipositone discrete fractional boundary value problem. Arch. Math. 99, 509–518 (2012). https://doi.org/10.1007/s00013-012-0463-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-012-0463-2

Mathematics Subject Classification (2010)

Keywords

Search

Navigation