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Czechoslovak Mathematical Journal

, Volume 61, Issue 1, pp 127–144 | Cite as

Multiple positive solutions to multipoint one-dimensional p-Laplacian boundary value problem with impulsive effects

  • Yuansheng Tian
  • Anping Chen
  • Weigao Ge
Article

Abstract

In this paper, using a fixed point theorem on a convex cone, we consider the existence of positive solutions to the multipoint one-dimensional p-Laplacian boundary value problem with impulsive effects, and obtain multiplicity results for positive solutions.

Keywords

p-Laplacian operator boundary value problem impulsive differential equations fixed-point theorem positive solutions 

MSC 2010

34B15 34B18 34B37 

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References

  1. [1]
    Z. Bai, W. Ge: Existence of three positive solutions for some second-order boundary value problems. Comput. Math. Appl. 48 (2004), 699–707.CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    L. Chen, J. Sun: Nonlinear boundary value problem of first order impulsive functional differential equations. J. Math. Anal. Appl. 318 (2006), 726–741.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    W. Ding, M. Han: Periodic boundary value problem for the second order impulsive functional differential equations. Appl. Math. Comput. 155 (2004), 709–726.CrossRefMATHMathSciNetGoogle Scholar
  4. [4]
    E.R. Kaufmann, N. Kosmatov, Y.N. Raffoul: A second-order boundary value problem with impulsive effects on an unbounded domain. Nonlinear Anal., Theory Methods Appl. 69 (2008), 2924–2929.CrossRefMATHMathSciNetGoogle Scholar
  5. [5]
    X. Lin, D. Jiang: Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations. J. Math. Anal. Appl. 321 (2006), 501–514.CrossRefMATHMathSciNetGoogle Scholar
  6. [6]
    Y.-H. Lee, X. Liu: Study of singular boundary value problems for second order impulsive differential equations. J. Math. Anal. Appl. 331 (2007), 159–176.CrossRefMATHMathSciNetGoogle Scholar
  7. [7]
    E.K. Lee, Y.-H. Lee: Multiple positive solutions of singular two point boundary value problems for second order impulsive differential equation. Appl. Math. Comput. 158 (2004), 745–759.CrossRefMATHMathSciNetGoogle Scholar
  8. [8]
    I. Rachůnková, J. Tomeček: Singular Dirichlet problem for ordinary differential equation with impulses. Nonlinear Anal., Theory Methods Appl. 65 (2006), 210–229.CrossRefMATHGoogle Scholar
  9. [9]
    I. Rachůnková, M. Tvrdý: Second-order periodic problem with φ-Laplacian and impulses. Nonlinear Anal., Theory Methods Appl. 63 (2005), 257–266.CrossRefGoogle Scholar
  10. [10]
    H. Su, Z. Wei, B. Wang: The existence of positive solutions for a nonlinear four-point singular boundary value problem with a p-Laplacian operator. Nonlinear Anal., Theory Methods Appl. 66 (2007), 2204–2217.CrossRefMATHMathSciNetGoogle Scholar
  11. [11]
    J. Shen, W. Wang: Impulsive boundary value problems with nonlinear boundary conditions. Nonlinear Anal., Theory Methods Appl. 69 (2008), 4055–4062.CrossRefMATHMathSciNetGoogle Scholar
  12. [12]
    Y. Tian, D. Jiang, W. Ge: Multiple positive solutions of periodic boundary value problems for second order impulsive differential equations. Appl. Math. Comput. 200 (2008), 123–132.CrossRefMATHMathSciNetGoogle Scholar
  13. [13]
    Y. Wang, C. Hou: Existence of multiple positive solutions for one dimensional p-Laplacian. J. Math. Anal. Appl. 315 (2006), 144–153.CrossRefMATHMathSciNetGoogle Scholar
  14. [14]
    X. Zhang, W. Ge: Impulsive boundary value problems involving the one-dimensional p-Laplacian. Nonlinear Anal., Theory Methods Appl. 70 (2009), 1692–1701.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2011

Authors and Affiliations

  1. 1.ChenzhouChina
  2. 2.BeijingChina
  3. 3.Department of MathematicsXiangnan UniversityChenzhou, HunanP.R.China
  4. 4.Department of MathematicsBeijing Institute of TechnologyBeijingP.R.China

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