Skip to main content
Log in

Multiplicity results for a two-point boundary value double eigenvalue problem

  • Published:
Ricerche di Matematica Aims and scope Submit manuscript

Abstract

The purpose of this note is to prove the existence of three solutions for a two-point boundary value double eigenvalue problem. The approach is fully based on a recent three critical points theorem of B. Ricceri [A three critical points theorem revisited, Nonlinear Anal., 70/9 (2009) 3084–3089].

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. Afrouzi G.A., Heidarkhani S.: Three solutions for a quasilinear boundary value problem. Nonlinear Anal. 69, 3330–3336 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Anello G., Cordaro G.: Positive infinitely many arbitrarily small solutions for the Dirichlet problem involving the p-Laplacian. Proc. R. Soc. Edinb. Sect. A. 132, 511–519 (2002)

    Article  MathSciNet  Google Scholar 

  3. Bonanno G.: A Critical points theorem and nonlinear differential problems. J. Glob. Optim. 28, 249–258 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bonanno G.: Existence of three solutions for a two point boundary value problem. Appl. Math. Lett. 13, 53–57 (2000)

    Article  MathSciNet  Google Scholar 

  5. Bonanno G.: Some remarks on a three critical points theorem. Nonlinear Anal. 54, 651–665 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Candito, P.: Existence of three solutions for a nonautonomous two point boundary value problem. J. Math. Anal. Appl. 252, 532–537 (2000). Appl. 277, 180–189 (2003)

    Google Scholar 

  7. Heidarkhani, S., Motreanu, D.: Multiplicity results for a two-point boundary value problem, preprint

  8. Livrea R.: Existence of three solutions for a quasilinear two point boundary value problem. Arch. Math. 79, 288–298 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Marano S.A., Motreanu D.: On a three critical points theorem for non-differentiable functions and applications to nonlinear boundary value problems. Nonlinear Anal. 48, 37–52 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ricceri B.: On a three critical points theorem. Arch. Math. (Basel) 75, 220–226 (2000)

    MATH  MathSciNet  Google Scholar 

  11. Ricceri B.: A three critical points theorem revisited. Nonlinear Anal. 70(9), 3084–3089 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ricceri B.: Three solutions for a Neumann problem. Topol. Methods Nonlinear Anal. 20, 257–281 (2002)

    MathSciNet  Google Scholar 

  13. Zeidler E.: Nonlinear functional analysis and its applications, vol. II. Springer, Berlin-Heidelberg- New York (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. A. Afrouzi.

Additional information

Communicated by Editor in Chief.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Afrouzi, G.A., Heidarkhani, S. Multiplicity results for a two-point boundary value double eigenvalue problem. Ricerche mat. 59, 39–47 (2010). https://doi.org/10.1007/s11587-010-0072-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11587-010-0072-y

Keywords

Mathematics Subject Classification (2000)

Navigation