Skip to main content

Positive Solutions of Boundary Value Problems for System of Nonlinear Fourth-Order Differential Equations

Abstract

Some existence theorems of the positive solutions and the multiple positive solutions for singular and nonsingular systems of nonlinear fourth-order boundary value problems are proved by using topological degree theory and cone theory.

[12345678910111213]

References

  1. Gupta CP: Existence and uniqueness theorems for the bending of an elastic beam equation. Applicable Analysis 1988,26(4):289-304. 10.1080/00036818808839715

    Article  MATH  MathSciNet  Google Scholar 

  2. Gupta CP: Existence and uniqueness results for the bending of an elastic beam equation at resonance. Journal of Mathematical Analysis and Applications 1988,135(1):208-225. 10.1016/0022-247X(88)90149-7

    Article  MATH  MathSciNet  Google Scholar 

  3. Agarwal RP: On fourth order boundary value problems arising in beam analysis. Differential Integral Equations 1989,2(1):91-110.

    MATH  MathSciNet  Google Scholar 

  4. O'Regan D: Solvability of some fourth (and higher) order singular boundary value problems. Journal of Mathematical Analysis and Applications 1991,161(1):78-116. 10.1016/0022-247X(91)90363-5

    Article  MATH  MathSciNet  Google Scholar 

  5. Yang YS: Fourth-order two-point boundary value problems. Proceedings of the American Mathematical Society 1988,104(1):175-180. 10.1090/S0002-9939-1988-0958062-3

    Article  MATH  MathSciNet  Google Scholar 

  6. Ma R, Wang H: On the existence of positive solutions of fourth-order ordinary differential equations. Applicable Analysis 1995,59(1–4):225-231.

    MATH  MathSciNet  Google Scholar 

  7. Wei ZL, Zhang ZT: A necessary and sufficient condition for the existence of positive solutions of singular superlinear boundary value problems. Acta Mathematica Sinica 2005,48(1):25-34.

    MATH  MathSciNet  Google Scholar 

  8. Wei ZL: Positive solutions to singular boundary value problems for a class of fourth-order sublinear differential equations. Acta Mathematica Sinica 2005,48(4):727-738.

    MATH  MathSciNet  Google Scholar 

  9. Li YX: Existence and multiplicity of positive solutions for fourth-order boundary value problems. Acta Mathematicae Applicatae Sinica 2003,26(1):109-116.

    MATH  MathSciNet  Google Scholar 

  10. Zhou YM: Positive solutions to fourth-order nonlinear eigenvalue problems. Journal of Systems Science and Mathematical Sciences 2004,24(4):433-442.

    MATH  MathSciNet  Google Scholar 

  11. Guo DJ: Nonlinear Functional Analysis. Science and Technology Press, Jinan, Shandong, China; 1985.

    Google Scholar 

  12. Guo DJ, Lakshmikantham V: Nonlinear Problems in Abstract Cones, Notes and Reports in Mathematics in Science and Engineering. Volume 5. Academic Press, Boston, Mass, USA; 1988:viii+275.

    Google Scholar 

  13. Cheng JG: Nonlinear singular boundary value problems. Acta Mathematicae Applicatae Sinica 2000,23(1):122-129.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shengli Xie.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Xie, S., Zhu, J. Positive Solutions of Boundary Value Problems for System of Nonlinear Fourth-Order Differential Equations. Bound Value Probl 2007, 076493 (2007). https://doi.org/10.1155/2007/76493

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/2007/76493

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Existence Theorem