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Positive solutions for third order multi-point singular boundary value problems

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Abstract

We study a third order singular boundary value problem with multi-point boundary conditions. Sufficient conditions are obtained for the existence of positive solutions of the problem. Recent results in the literature are significantly extended and improved. Our analysis is mainly based on a nonlinear alternative of Leray-Schauder.

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References

  1. R.P. Agarwal and D. O’Regan: Singular Differential and Integral Equations with Applications. Kluwer Academic Publishers, Boston, 2003.

    MATH  Google Scholar 

  2. R.P. Agarwal and D. O’Regan: Positive solutions for (p, n-p) conjugate boundary value problems. J. Differential Equations 150 (1998), 462–473.

    Article  MATH  MathSciNet  Google Scholar 

  3. R. P. Agarwal and D. O’Regan: Singular boundary value problems for superlinear second order ordinary and delay differential equations. J. Differential Equations 130 (1996), 333–355.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. Chu, P. J. Torres and M. Zhang: Periodic solutions of second order non-autonomous singular dynamical systems. J. Differential Equations 239 (2007), 196–211.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. A. Gatica, V. Oliver and P. Waltman: Singular nonlinear boundary value problems for second order differential equations. J. Differential Equations 79 (1989), 62–78.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. R. Graef, J. Henderson and B. Yang: Positive solutions to a singular third order nonlocal boundary value problem. Indian J. Math. 50 (2008), 317–330.

    MATH  MathSciNet  Google Scholar 

  7. J. R. Graef, J. Henderson and B. Yang: Existence of positive solutions of a higher order nonlocal singular boundary value problem. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 16, Supplement S1 (2009), 147–152.

    MATH  MathSciNet  Google Scholar 

  8. J. R. Graef and B. Yang: Positive solutions of a third order nonlocal boundary value problem. Discrete Contin. Dyn. Syst. Ser. S 1 (2008), 89–97.

    MATH  MathSciNet  Google Scholar 

  9. P. W. Eloe and J. Henderson: Singular nonlinear (k, n - k) conjugate boundary value problems. J. Differential Equations 133 (1997), 136–151.

    Article  MATH  MathSciNet  Google Scholar 

  10. P. W. Eloe and J. Henderson: Singular nonlinear boundary value problems for higher order ordinary differential equations. Nonlinear Anal. 17 (1991), 1–10.

    Article  MATH  MathSciNet  Google Scholar 

  11. M. Maroun: Positive solutions to an Nth order right focal boundary value problem. Electron. J. Qual. Theory Diff. Equ. 2007, 17 (electronic).

  12. M. Maroun: Positive solutions to an third-order right focal boundary value problem. Comm. Appl. Nonlinear Anal. 12 (2005), 71–82.

    MATH  MathSciNet  Google Scholar 

  13. L. Kong and Q. Kong: Positive solutions of higher-order boundary value problems. Proc. Edinburgh Math. Soc. 48 (2005), 445–464.

    Article  MATH  Google Scholar 

  14. I. Rachůnková and S. Staněk: Sturm-Liouville and focal higher order BVPs with singularities in phase variables. Georgian Math. J. 10 (2003), 165–191.

    MATH  MathSciNet  Google Scholar 

  15. D. O’Regan: Existence of solutions to third order boundary value problems. Proc. Royal Irish Acad. Sect. A 90 (1990), 173–189.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, USA

    John R. Graef & Lingju Kong

  2. Department of Mathematics and Statistics, Kennesaw State University, Kennesaw, GA, 30144, USA

    Bo Yang

Authors
  1. John R. Graef
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  2. Lingju Kong
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  3. Bo Yang
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Correspondence to John R. Graef.

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Graef, J.R., Kong, L. & Yang, B. Positive solutions for third order multi-point singular boundary value problems. Czech Math J 60, 173–182 (2010). https://doi.org/10.1007/s10587-010-0007-5

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  • DOI: https://doi.org/10.1007/s10587-010-0007-5

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