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Positive Solutions of a Fractional Boundary Value Problem with Changing Sign Nonlinearity

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  • Yongqing Wang
  • Lishan Liu
  • Yonghong Wu

Abstract

We discuss the existence of positive solutions of a boundary value problem of nonlinear fractional differential equation with changing sign nonlinearity. We first derive some properties of the associated Green function and then obtain some results on the existence of positive solutions by means of the Krasnoselskii′s fixed point theorem in a cone.

Suggested Citation

  • Yongqing Wang & Lishan Liu & Yonghong Wu, 2012. "Positive Solutions of a Fractional Boundary Value Problem with Changing Sign Nonlinearity," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:149849
    DOI: 10.1155/2012/149849
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    References listed on IDEAS

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    1. Klaus Deimling, 1985. "Nonlinear Functional Analysis," Springer Books, Springer, number 978-3-662-00547-7, March.
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    Cited by:

    1. Xiangbing Zhou & Wenquan Wu & Hongjiang Ma, 2012. "A Contraction Fixed Point Theorem in Partially Ordered Metric Spaces and Application to Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Ge Bin, 2012. "Multiple Solutions for a Class of Fractional Boundary Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. J. Caballero & I. Cabrera & K. Sadarangani, 2012. "Positive Solutions of Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Jiqiang Jiang & Lishan Liu & Yonghong Wu, 2012. "Positive Solutions for Nonlinear Fractional Differential Equations with Boundary Conditions Involving Riemann‐Stieltjes Integrals," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Yulin Zhao & Guobing Ye & Haibo Chen, 2013. "Multiple Positive Solutions of a Singular Semipositone Integral Boundary Value Problem for Fractional q‐Derivatives Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Guotao Wang & Bashir Ahmad & Lihong Zhang, 2012. "On Impulsive Boundary Value Problems of Fractional Differential Equations with Irregular Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. Wei Wang & Li Huang, 2012. "Existence of Positive Solution for Semipositone Fractional Differential Equations Involving Riemann‐Stieltjes Integral Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    8. Hao Tao & Meichen Fu & Ru Qian, 2012. "Positive Solutions for Fractional Differential Equations from Real Estate Asset Securitization via New Fixed Point Theorem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

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