Open Access

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

Boundary Value Problems20082007:017951

DOI: 10.1155/2007/17951

Received: 3 May 2007

Accepted: 12 September 2007

Published: 8 January 2008

Abstract

Using fixed point index theory, we obtain several sufficient conditions of existence of at least one positive solution for third-order https://static-content.springer.com/image/art%3A10.1155%2F2007%2F17951/MediaObjects/13661_2007_Article_635_IEq1_HTML.gif -point boundary value problems.

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Authors’ Affiliations

(1)
College of Sciences, Hebei University of Science and Technology
(2)
College of Mathematics and Science of Information, Hebei Normal University

References

  1. Zhang X, Liu L, Wu C: Nontrivial solution of third-order nonlinear eigenvalue problems. Applied Mathematics and Computation 2006,176(2):714–721. 10.1016/j.amc.2005.10.017MATHMathSciNetView Article
  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 2004,294(1):104–112. 10.1016/j.jmaa.2004.02.001MATHMathSciNetView Article
  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 2006,322(2):735–748. 10.1016/j.jmaa.2005.09.065MATHMathSciNetView Article
  5. Jiang D, Agarwal RP: A uniqueness and existence theorem for a singular third-order boundary value problem on https://static-content.springer.com/image/art%3A10.1155%2F2007%2F17951/MediaObjects/13661_2007_Article_635_IEq2_HTML.gif . Applied Mathematics Letters 2002,15(4):445–451. 10.1016/S0893-9659(01)00157-4MATHMathSciNetView Article
  6. Anderson D, Avery RI: Multiple positive solutions to a third-order discrete focal boundary value problem. Computers & Mathematics with Applications 2001,42(3–5):333–340.MATHMathSciNetView Article
  7. Wang J, Gao W, Zhang Z: Singular nonlinear boundary value problems arising in boundary layer theory. Journal of Mathematical Analysis and Applications 1999,233(1):246–256. 10.1006/jmaa.1999.6290MATHMathSciNetView Article
  8. Paatashvili V, Samko S: Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in https://static-content.springer.com/image/art%3A10.1155%2F2007%2F17951/MediaObjects/13661_2007_Article_635_IEq3_HTML.gif . Boundary Value Problem 2005,2005(1):43–71. 10.1155/BVP.2005.43MATHMathSciNet
  9. Agarwal RP, Kiguradze I: Two-point boundary value problems for higher-order linear differential equations with strong singularities. Boundary Value Problems 2006, 2006: 32 pages.MathSciNetView Article

Copyright

© W. Jiang and F. Li 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.