Skip to main content

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

Abstract

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.

[123456789]

References

  1. 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.2005.10.017

    MATH  MathSciNet  Article  Google Scholar 

  2. 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. 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.2004.02.001

    MATH  MathSciNet  Article  Google Scholar 

  4. 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.2005.09.065

    MATH  MathSciNet  Article  Google Scholar 

  5. 5.

    Jiang D, Agarwal RP: A uniqueness and existence theorem for a singular third-order boundary value problem on . Applied Mathematics Letters 2002,15(4):445–451. 10.1016/S0893-9659(01)00157-4

    MATH  MathSciNet  Article  Google Scholar 

  6. 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.

    MATH  MathSciNet  Article  Google Scholar 

  7. 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.1999.6290

    MATH  MathSciNet  Article  Google Scholar 

  8. 8.

    Paatashvili V, Samko S: Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in . Boundary Value Problem 2005,2005(1):43–71. 10.1155/BVP.2005.43

    MATH  MathSciNet  Google Scholar 

  9. 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.

    MathSciNet  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Weihua Jiang.

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

Jiang, W., Li, F. Several Existence Theorems of Monotone Positive Solutions for Third-Order Multipoint Boundary Value Problems. Bound Value Probl 2007, 017951 (2008). https://doi.org/10.1155/2007/17951

Download citation

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Point Boundary