Open Access Research Article

Several Existence Theorems of Monotone Positive Solutions for Third-Order Multipoint Boundary Value Problems

Weihua Jiang1,2* and Fachao Li1

Author Affiliations

1 College of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China

2 College of Mathematics and Science of Information, Hebei Normal University, Shijiazhuang, Hebei 050016, China

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Boundary Value Problems 2007, 2007:017951 doi:10.1155/2007/17951


The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2007/1/017951


Received:3 May 2007
Accepted:12 September 2007
Published:8 January 2008

© 2007 Jiang and Li

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.

Using fixed point index theory, we obtain several sufficient conditions of existence of at least one positive solution for third-order -point boundary value problems.

References

  1. Zhang, X, Liu, L, Wu, C: Nontrivial solution of third-order nonlinear eigenvalue problems. Applied Mathematics and Computation. 176(2), 714–721 (2006). Publisher Full Text OpenURL

  2. Guo, L-J, Sun, J-P, Zhao, Y-H: Existence of positive solutions for nonlinear third-order three-point boundary value problems . to appear in Nonlinear Analysis: Theory, Methods & Applications

  3. Du, Z, Ge, W, Lin, X: Existence of solutions for a class of third-order nonlinear boundary value problems. Journal of Mathematical Analysis and Applications. 294(1), 104–112 (2004). Publisher Full Text OpenURL

  4. Cabada, A, Minhós, F, Santos, AI: Solvability for a third order discontinuous fully equation with nonlinear functional boundary conditions. Journal of Mathematical Analysis and Applications. 322(2), 735–748 (2006). Publisher Full Text OpenURL

  5. Jiang, D, Agarwal, RP: A uniqueness and existence theorem for a singular third-order boundary value problem on . Applied Mathematics Letters. 15(4), 445–451 (2002). Publisher Full Text OpenURL

  6. Anderson, D, Avery, RI: Multiple positive solutions to a third-order discrete focal boundary value problem. Computers & Mathematics with Applications. 42(3–5), 333–340 (2001). PubMed Abstract | Publisher Full Text OpenURL

  7. Wang, J, Gao, W, Zhang, Z: Singular nonlinear boundary value problems arising in boundary layer theory. Journal of Mathematical Analysis and Applications. 233(1), 246–256 (1999). Publisher Full Text OpenURL

  8. Paatashvili, V, Samko, S: Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in . Boundary Value Problem. 2005(1), 43–71 (2005). Publisher Full Text OpenURL

  9. Agarwal, RP, Kiguradze, I: Two-point boundary value problems for higher-order linear differential equations with strong singularities. Boundary Value Problems. 2006, 32 pages (2006)