Open Access Research Article

Existence of Positive Solutions for Fourth-Order Three-Point Boundary Value Problems

Chuanzhi Bai

Author Affiliations

Department of Mathematics, Huaiyin Teachers College, Huaian 223300, China

Boundary Value Problems 2006, 2007:068758  doi:10.1155/2007/68758


The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2007/1/068758


Received:11 July 2007
Accepted:7 November 2007
Published:20 January 2008

© 2006 Bai

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.

We are concerned with the nonlinear fourth-order three-point boundary value problem , , , , . By using Krasnoselskii's fixed point theorem in a cone, we get some existence results of positive solutions.

References

  1. Agarwal, RP: Focal Boundary Value problems for Differential and Difference Equations, Mathematics and Its Applications,p. x+289. Kluwer Academic Publishers, Dordrecht, The Netherlands (1998)

  2. Zill, DG, Cullen, MR: Differential Equations with Boundary-Value Problems, Brooks/Cole, Belmont, Calif, USA (2001)

  3. Bai, Z, Wang, H: On positive solutions of some nonlinear fourth-order beam equations. Journal of Mathematical Analysis and Applications. 270(2), 357–368 (2002). Publisher Full Text OpenURL

  4. Graef, JR, Yang, B: On a nonlinear boundary value problem for fourth order equations. Applicable Analysis. 72(3–4), 439–448 (1999)

  5. Hao, Z, Liu, L, Debnath, L: A necessary and sufficient condition for the existence of positive solutions of fourth-order singular boundary value problems. Applied Mathematics Letters. 16(3), 279–285 (2003). Publisher Full Text OpenURL

  6. Li, F, Zhang, Q, Liang, Z: Existence and multiplicity of solutions of a kind of fourth-order boundary value problem. Nonlinear Analysis: Theory, Methods & Applications. 62(5), 803–816 (2005). PubMed Abstract | Publisher Full Text OpenURL

  7. Liu, B: Positive solutions of fourth-order two point boundary value problems. Applied Mathematics and Computation. 148(2), 407–420 (2004). Publisher Full Text OpenURL

  8. Yang, D, Zhu, H, Bai, C: Positive solutions for semipositone fourth-order two-point boundary value problems. Electronic Journal of Differential Equations.(16), 1–8 (2007)

  9. Ma, R: Positive solutions of fourth-order two-point boundary value problems. Annals of Differential Equations. 15(3), 305–313 (1999)

  10. Torres, PJ: Existence of one-signed periodic solutions of some second-order differential equations via a Krasnosel'skii fixed point theorem. Journal of Differential Equations. 190(2), 643–662 (2003). Publisher Full Text OpenURL

  11. Krasnosel'skii, MA: Positive Solutions of Operator Equations,p. 381. P. Noordhoff, Groningen, The Netherlands (1964)