Open Access

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

Boundary Value Problems20072007:076493

DOI: 10.1155/2007/76493

Received: 23 March 2006

Accepted: 5 December 2006

Published: 30 January 2007


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.


Authors’ Affiliations

Department of Mathematics, Suzhou College
School of Mathematics Science, Xuzhou Normal University


  1. Gupta CP: Existence and uniqueness theorems for the bending of an elastic beam equation. Applicable Analysis 1988,26(4):289-304. 10.1080/00036818808839715MATHMathSciNetView ArticleGoogle 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)90149-7MATHMathSciNetView ArticleGoogle Scholar
  3. Agarwal RP: On fourth order boundary value problems arising in beam analysis. Differential Integral Equations 1989,2(1):91-110.MATHMathSciNetGoogle 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)90363-5MATHMathSciNetView ArticleGoogle Scholar
  5. Yang YS: Fourth-order two-point boundary value problems. Proceedings of the American Mathematical Society 1988,104(1):175-180. 10.1090/S0002-9939-1988-0958062-3MATHMathSciNetView ArticleGoogle 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.MATHMathSciNetGoogle 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.MATHMathSciNetGoogle 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.MATHMathSciNetGoogle 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.MATHMathSciNetGoogle Scholar
  10. Zhou YM: Positive solutions to fourth-order nonlinear eigenvalue problems. Journal of Systems Science and Mathematical Sciences 2004,24(4):433-442.MATHMathSciNetGoogle 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.MATHMathSciNetGoogle Scholar


© S. Xie and J. Zhu. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.