Skip to main content
SpringerLink
Log in

Solution and positive solution of a semilinear third-order equation

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

Abstract

In this paper, the boundary value problem of a semilinear third-order equation is considered. Making use of the upper and lower solutions method and a new maximum principle, the existence results and iterative formula of solution and positive solution are 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. Klaasen, G.: Differential inequalities and existence theorems for second and third order boundary value problems. J. Differ. Equ. 10, 529–537 (1971)

    Article  MathSciNet  Google Scholar 

  2. Greguš, M.: Third order linear differential equations. In: Mathematics and Its Applications. Reidel, Dordrecht (1987)

    Google Scholar 

  3. O’Regan, D.: Topological transversality: application to third-order boundary vale problem. SIAM J. Math. Anal. 19, 630–641 (1987)

    Article  Google Scholar 

  4. Troy, W.C.: Solution of third order differential equations relevant to draining and coating flows. SIAM J. Math. Anal. 24, 155–171 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cabada, A.: The method of lower and upper solutions for second, third, fourth and higher order boundary value problems. J. Math. Anal. Appl. 185, 302–320 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ma, R.: Multiplicity results for a third order boundary value problem at resonance. Nonlinear Anal. 32, 493–500 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bartušek, M., Cecchi, M., Marini, M.: On Kneser solution of nonlinear third order differential equations. J. Math. Anal. Appl. 261, 72–84 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Yao, Q., Feng, Y.: The existence of solutions for a third order two-point boundary value problem. Appl. Math. Lett. 15, 227–232 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ladde, G.S., Lakshmikantham, V., Vatsala, A.S.: Monotone Iterative Techniques for Nonlinear Differential Equations. Pitman, Boston (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Science, Wuhan University of Science and Technology, Wuhan, 430065, China

    Yuqiang Feng

Authors
  1. Yuqiang Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuqiang Feng.

Additional information

This research is supported by China National Science Foundation under Grant No. 60574075 and Nature Science Foundation of Education Committee of Hu Bei Province under Grant No. Q20061101.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feng, Y. Solution and positive solution of a semilinear third-order equation. J. Appl. Math. Comput. 29, 153–161 (2009). https://doi.org/10.1007/s12190-008-0121-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-008-0121-9

Keywords

Mathematics Subject Classification (2000)

Search

Navigation