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Existence and multiplicity of positive and negative solutions for higher-order multi-point Sturm-Liouville boundary value problems

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References

  1. R. P. Agarwal, “ Focal Boundary Value Problems for Differential and Difference Equations”, Kluwer Academic, Dordrecht, 1998.

    MATH  Google Scholar 

  2. R. P. Agarwal, D. O’Regan, and P. J.Y. Wong, “ Positive Solutions of Differential, Difference, and Integral Equations”, Kluwer Academic, Dordrecht, 1998.

    Google Scholar 

  3. R. Agarwal and D. O’Regan, Nonlinear superlinear singular and nonsingular second order boundary value problems, J. Differential Equations, 143(1998), 60–95.

    Article  MATH  MathSciNet  Google Scholar 

  4. D. R. Anderson and J. M. Davis, Multiple solutions and eigenvalues for third-order right focal boundary-value problem, J. Math. Anal. Appl., 267(2002), 135–157.

    Article  MATH  MathSciNet  Google Scholar 

  5. Z. Bai and H. Wang, On positive solutions of some nonlinear fourth-order beam equations, J. Math. Anal. Appl., 270(2002), 357–368.

    Article  MATH  MathSciNet  Google Scholar 

  6. W. A. Copel, “Stability and Asymptotic Behavior of Differential Equations”, Heath & Co., Boston, 1965.

    Google Scholar 

  7. J. M. Davis, L. H. Erbe, and J. Henderson, Multiplicity of positive solutions for higher order Sturm-Liouville problems, Rocky Mountain J. Math., 31(2001), 169–184.

    Article  MATH  MathSciNet  Google Scholar 

  8. Y. Cui and Y. Zou, Positive solutions of singular fourth-order boundary value problems, Electron. J. Differential Equations Vol. 2006(2006), No.39, 1–10.

    MathSciNet  Google Scholar 

  9. L. H. Erbe and M. Tang, Existence and multiplicity of positive solutions to nonlinear boundary value problems, Differential Equations and Dynamical Systems, 4(1996), 313–320.

    MATH  MathSciNet  Google Scholar 

  10. L. H. Erbe and H. Wang, On existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc., 120(1994), 743–748.

    Article  MATH  MathSciNet  Google Scholar 

  11. L. H. Erbe and K. Schmitt, Boundary value problems for second order differential equations, Lectures Notes in Pure and Appl. Math., 109(1987), 179–184.

    MathSciNet  Google Scholar 

  12. J. Ge and C. Bai, Solvability of a four-point boundary-value problem for fourth-order ordinary, Electr. J. Differential Equations, Vol. 2007(2007), No. 123, 1–9.

    MathSciNet  Google Scholar 

  13. J. R. Graef, J. Henderson, and B. Yang, Existence and nonexistence of positive solutions of an n-th order nonlocal boundary value problem, Proceedings of the 5th International Conference on Dynamic Systems and Applications 1, 2007.

  14. J. R. Graef and B. Yang, On a nonlinear boundary-value problem for fourth order equations, Appl. Anal., 72(1999), 439–448.

    Article  MATH  MathSciNet  Google Scholar 

  15. J. R. Graef and B. Yang, Positive solutions to a multi-point higher order boundary-value problem, J. Math. Anal. Appl., 316(2006), 409–421.

    Article  MATH  MathSciNet  Google Scholar 

  16. J. R. Graef, J. Henderson, and B. Yang, Positive solutions of a nonlinear higher order boundary-value problem, Electr. J. Differential Equations, Vol. 2007(2007), No. 45, 1–10.

    MathSciNet  Google Scholar 

  17. J. R. Graef, C. Qianz, and Bo Yang, Multiple positive solutions of a boundary value problem for ordinary differential equations, Electr. J. Qualitative Theory of Differential Equations, Proc. 7th Coll. QTDE, 11(2004), 1–13.

    Google Scholar 

  18. Z. Hao, L. Liu, and L. Debnath, A necessary and sufficient condition for the existence of positive solution of fourth-order singular boundary-value problems, Appl. Math. Lett., 16(2003), 279–285.

    Article  MATH  MathSciNet  Google Scholar 

  19. D. O’Regan, “ Theory of Singular Boundary Value Problems”, World Scientific, Singapore, 1994.

    MATH  Google Scholar 

  20. P. K. Palamides, Boundary and periodic value problems for differential systems via Sperner’s lemma, Math. Japonica, No. 1, (1989), 89–110.

  21. P. K. Palamides, Positive solutions for higher-order Sturm-Liouville problems, A new approach via vector field, Differential Equations and Dynamical Systems, 9(2002), 83–103.

    Google Scholar 

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Palamides, A.P. Existence and multiplicity of positive and negative solutions for higher-order multi-point Sturm-Liouville boundary value problems. Differ Equ Dyn Syst 16, 121–143 (2008). https://doi.org/10.1007/s12591-008-0008-0

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