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  • Research Article
  • Open Access

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

Boundary Value Problems20082007:068758

  • Received: 11 July 2007
  • Accepted: 7 November 2007
  • Published:


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.


  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Point Theorem


Authors’ Affiliations

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


  1. Agarwal RP: Focal Boundary Value problems for Differential and Difference Equations, Mathematics and Its Applications. Volume 436. Kluwer Academic Publishers, Dordrecht, The Netherlands; 1998:x+289.View ArticleGoogle Scholar
  2. Zill DG, Cullen MR: Differential Equations with Boundary-Value Problems. 5th edition. Brooks/Cole, Belmont, Calif, USA; 2001.Google Scholar
  3. Bai Z, Wang H: On positive solutions of some nonlinear fourth-order beam equations. Journal of Mathematical Analysis and Applications 2002,270(2):357–368. 10.1016/S0022-247X(02)00071-9MATHMathSciNetView ArticleGoogle Scholar
  4. Graef JR, Yang B: On a nonlinear boundary value problem for fourth order equations. Applicable Analysis 1999,72(3–4):439–448.MATHMathSciNetView ArticleGoogle Scholar
  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 2003,16(3):279–285. 10.1016/S0893-9659(03)80044-7MATHMathSciNetView ArticleGoogle Scholar
  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 2005,62(5):803–816. 10.1016/ ArticleGoogle Scholar
  7. Liu B: Positive solutions of fourth-order two point boundary value problems. Applied Mathematics and Computation 2004,148(2):407–420. 10.1016/S0096-3003(02)00857-3MATHMathSciNetView ArticleGoogle Scholar
  8. Yang D, Zhu H, Bai C: Positive solutions for semipositone fourth-order two-point boundary value problems. Electronic Journal of Differential Equations 2007, (16):1–8.Google Scholar
  9. Ma R: Positive solutions of fourth-order two-point boundary value problems. Annals of Differential Equations 1999,15(3):305–313.MATHMathSciNetGoogle Scholar
  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 2003,190(2):643–662. 10.1016/S0022-0396(02)00152-3MATHMathSciNetView ArticleGoogle Scholar
  11. Krasnosel'skii MA: Positive Solutions of Operator Equations. P. Noordhoff, Groningen, The Netherlands; 1964:381.Google Scholar


© Bai 2006

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