Skip to main content
SpringerLink
Log in

Eigenvalue for a singular second order three-point boundary value problem

  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

In this paper, the existence of positive solutions for a singular second-order three-point boundary value problem is investigated. By using Krasnoselskii’s fixed point theorem, several sufficient conditions for the existence of positive solutions and the eigenvalue intervals on which there exist positive solutions are obtained. Finally, two examples are given to illustrate the importance of results obtained.

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. Moshinsky, M.: Sobre los problemas de condiciones a la frontiera en una dimension de caracteristicas discontinuas. Bol. Soc. Mat. Mexicana 7, 10–25 (1950)

    MathSciNet  Google Scholar 

  2. Timoshenko, S.: Theory of Elastic Stability. McGraw-Hill, New York (1961)

    Google Scholar 

  3. Zou, Y., Hu, Q., Zhang, R.: On numerical studies of multi-point boundary value problem and its fold bifurcation. Appl. Math. Comput. 185, 527–537 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. II’in, V.A., Moiseev, E.I.: Nonlocal boundary value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects. Differ. Equ. 23, 803–810 (1987)

    Google Scholar 

  5. II’in, V.A., Moiseev, E.I.: Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator. Differ. Equ. 23, 979–987 (1987)

    Google Scholar 

  6. Gupta, C.P.: Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation. J. Math. Anal. Appl. 168, 540–551 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  7. Xue, C., Du, Z., Ge, W.: Solutions to m-point boundary value problems of third order ordinary differential equations at resonance. J. Appl. Math. Comput., Int. J. 17, 229–244 (2004)

    Article  MathSciNet  Google Scholar 

  8. Xue, C., Du, Z., Ge, W.: Multi-point boundary value problems for one-dimensional p-Laplace at resonance. J. Appl. Math. Comput., Int. J. 22, 361–372 (2006)

    Article  Google Scholar 

  9. Liu, Y.: Solutions of Sturm-Liouville type Multi-point boundary value problems for higher-order differential equations. J. Appl. Math. Comput., Int. J. 23, 167–182 (2007)

    Article  MATH  Google Scholar 

  10. Feng, H., Ge, W.: Existence of triple symmetric positive solutions for four-point boundary-value problem with one-dimensional p-Laplacian. J. Appl. Math. Comput., Int. J. 27, 325–337 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Palamides, P.K., Infante, G., Pietramala, P.: Nontrivial solutions of a nonlinear heat flow problem via Sperner’s Lemma. Appl. Math. Lett. 22, 1444–1450 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ma, R.: Multiplicity of positive solutions for second-order three-point boundary value problems. Comput. Math. Appl. 40, 193–204 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. Agarwal, R.P., O’Regan, D.: Multiple nonnegative solutions for second order impulsive differential equations. Appl. Math. Comput. 114, 51–59 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  14. Guo, D., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones. Academic Press, Orlando (1988)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, 050003, Hebei, P.R. China

    Donglong Bai & Hanying Feng

Authors
  1. Donglong Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hanying Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hanying Feng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bai, D., Feng, H. Eigenvalue for a singular second order three-point boundary value problem. J. Appl. Math. Comput. 38, 443–452 (2012). https://doi.org/10.1007/s12190-011-0489-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-011-0489-9

Keywords

Mathematics Subject Classification (2000)

Search

Navigation