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Existence of multiple positive solutions for nth-order p-Laplacian m-point singular boundary value problems

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Abstract

In this paper, by using fixed point theorem, we prove the existence of multiple positive solutions for a class of nth-order p-Laplacian m-point singular boundary value problem. The interesting point is that the nonlinear term f explicitly involves the each-order derivative of variable u(t).

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References

  1. Feng, H., Ge, W.: Triple symmetric positive solutions for multipoint boundary-value problem with one-dimensional p-Laplacian. Math. Comput. Modell. 47, 186–195 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Feng, H., Ge, W.: Existence of three positive solutions for m-point boundary-value problems with one-dimensional p-Laplacian. Nonlinear Anal. 68, 2017–2026 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  3. Fenga, H., Ge, W., Jiang, M.: Multiple positive solutions for m-point boundary-value problems with a one-dimensional p-Laplacian. Nonlinear Anal. 68, 2269–2279 (2008)

    Article  MathSciNet  Google Scholar 

  4. Feng, W., Webb, J.R.L.: Solvability of m-point boundary value problem with nonlinear growth. J. Math. Appl. 212, 467–480 (1997)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. Guo, Y., Ji, Y., Liu, X.: Multiple positive solutions for some multi-point boundary value problems with p-Laplacian. J. Comput. Appl. Math. 216, 144–156 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gupta, C.P.: A generalized multi-point boundary value problem for second order ordinary differential equation. Appl. Math. Comput. 89, 138–146 (1998)

    Article  Google Scholar 

  8. Jiang, W.: Multiple positive solutions for nth-order m-point boundary value problems with all derivatives. Nonlinear Anal. 68, 1064–1072 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ma, R., O’Regan, D.: Solvability of singular second order m-point boundary value problems. J. Math. Appl. 301, 124–134 (2005)

    MATH  MathSciNet  Google Scholar 

  10. Pang, C., Dong, W., Wei, Z.: Green’s function and positive solutions of nth order m-point boundary value problem. Appl. Math. Comput. 182, 1231–1239 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. O’Regan, D.: Theory of Singular Boundary Value Problems. World Scientific, Singapore (1994)

    MATH  Google Scholar 

  12. O’Regan, D.: Singular Dirichlet boundary value problems—I. Super-linear and non-resonance case. Nonlinear Anal. TMA 29(2), 221–245 (1997)

    Article  MATH  Google Scholar 

  13. Su, H.: Positive solutions for n-order m-point p-Laplacian operator singular boundary value problems. Appl. Math. Comput. 199, 122–132 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  14. Sun, B., Qu, Y., Ge, W.G.: Existence and iteration of positive solutions for a multipoint one-dimensional p-Laplacian boundary value problem. Appl. Math. Comput. 197, 389–398 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  15. Taliaferro, S.D.: A nonlinear singular boundary value problem. Nonlinear Anal. TMA 3, 897–904 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  16. Wei, Z., Pang, C.: Positive solutions of non-resonant singular boundary value problem of second order differential equations. Nagoya Math. J. 162, 127–148 (2001)

    MATH  MathSciNet  Google Scholar 

  17. Wei, Z.: A class of fourth order singular boundary value problems. Appl. Math. Comput. V 153(3), 865–884 (2004)

    Article  MATH  Google Scholar 

  18. Zhang, Y.: Positive solutions of singular sub-linear Emden–Fowler boundary value problems. J. Math. Anal. Appl. 185, 215–222 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  19. Zhang, G., Sun, J.: Positive solutions of m-point boundary value problem. J. Math. Anal. Appl. 291, 406–418 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  20. Zhu, Y., Wang, K.: On the existence of solutions of p-Laplacian m-point boundary value problem at resonance. Nonlinear Anal. 70, 1557–1564 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  21. Guo, D.J.: Nonlinear Functional Analysis. Shandong Sci. and Tech. Press, Jinan (1985) (in Chinese)

    Google Scholar 

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Authors and Affiliations

  1. Xuzhou Higher Normal School, Xuzhou, 221116, People’s Republic of China

    Yunzhou Zhu

  2. Department of Mathematics, Xuzhou Normal University, Xuzhou, 221116, People’s Republic of China

    Jiang Zhu

Authors
  1. Yunzhou Zhu
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  2. Jiang Zhu
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Correspondence to Jiang Zhu.

Additional information

This work was supported by the NNSF of China (10671167,10771212).

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Zhu, Y., Zhu, J. Existence of multiple positive solutions for nth-order p-Laplacian m-point singular boundary value problems. J. Appl. Math. Comput. 34, 393–405 (2010). https://doi.org/10.1007/s12190-009-0329-3

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  • DOI: https://doi.org/10.1007/s12190-009-0329-3

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