Skip to main content


You are viewing the new article page. Let us know what you think. Return to old version

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


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.



  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

  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

  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

  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

  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.

  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

  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

  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.

Download references

Author information

Correspondence to Weihua Jiang.

Rights and permissions

Reprints and Permissions

About this article


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