Skip to main content
Log in

Infinitely Many Solutions for a Class of Fractional Boundary Value Problems with Dirichlet Boundary Conditions

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

Abstract

In this paper we prove the existence and multiplicity of weak solutions for a class of fractional boundary value problem. Our approach is based on a critical point result contained in Bonanno and Molica Bisci [Bound. Value. Probl. 2009, 1–20 (2009)].

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.

Similar content being viewed by others

References

  1. El-Sayed A.M.A.: Nonlinear functional differential equations of arbitrary orders. Nonlinear Anal. 3, 181–186 (1998)

    Article  MathSciNet  Google Scholar 

  2. Kilbas A.A., Trujillo J.J.: Differential equations of fractional order: methods, results and problems I. Appl. Anal. 78, 153–192 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Kilbas A.A., Trujillo J.J.: Differential equations of fractional order: methods, results and problems II. Appl. Anal. 81, 435–493 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Podlubny I.: Fractional Differential Equations. Academic Press, New York (1999)

    MATH  Google Scholar 

  5. Samko G., Kilbas A., Marichev O.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Amsterdam (1993)

    MATH  Google Scholar 

  6. Lakshmikantham V., Vatsala A.S.: Basic theory of fractional differential equations. Nonlinear Anal. TMA 69(8), 2677–2682 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  7. Jiao F., Zhou Y.: Existence of solutions for a class of fractional boundary value problems via critical point theory. Comput. Math. Appl. 62, 1181–1199 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chen, J., Tang, X.H.: Existence and multiplicity of solutions for some fractional boundary value problem via critical point theory. Abstr. Appl. Anal., Article ID 648635 (2012)

  9. Teng, K., Jia, H., Zhang, H.: Existence and multiplicity results for fractional differential inclusions with Dirichlet boundary conditions. Appl. Math. Comput. (2012, Preprint)

  10. Nyamoradi, N.: Multiplicity results for a class of fractional boundary value problems. Annales Polonici Mathematici (preprint)

  11. Sun, H.R., Zhang, Q.G.: Existence of solutions for fractional boundary value problem via the Mountain Pass method and an iterative technique. Comput. Math. Appl. (2012, Preprint)

  12. Bonanno, G., Molica Bisci, G.: Infinitely many solutions for a boundary value problem with discontinuous nonlinearities. Bound. Value Probl. 2009, 1–20 (2009)

    Article  MathSciNet  Google Scholar 

  13. Ricceri B.: A general variational principle and some of its applications. J. Comput. Appl. Math. 133, 401–410 (2000)

    Article  MathSciNet  Google Scholar 

  14. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. In: North-Holland Mathematics Studies, vol. 204. Elsevier Science B.V., Amsterdam (2006)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nemat Nyamoradi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nyamoradi, N. Infinitely Many Solutions for a Class of Fractional Boundary Value Problems with Dirichlet Boundary Conditions. Mediterr. J. Math. 11, 75–87 (2014). https://doi.org/10.1007/s00009-013-0307-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00009-013-0307-8

Mathematics Subject Classification

Keywords

Navigation