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Positive Solutions of Eigenvalue Problems for a Class of Fractional Differential Equations with Derivatives

Author

Listed:
  • Xinguang Zhang
  • Lishan Liu
  • Benchawan Wiwatanapataphee
  • Yonghong Wu

Abstract

By establishing a maximal principle and constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of a class of fractional differential equations is discussed. Some sufficient conditions for the existence of positive solutions are established.

Suggested Citation

  • Xinguang Zhang & Lishan Liu & Benchawan Wiwatanapataphee & Yonghong Wu, 2012. "Positive Solutions of Eigenvalue Problems for a Class of Fractional Differential Equations with Derivatives," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:512127
    DOI: 10.1155/2012/512127
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    References listed on IDEAS

    as
    1. Yige Zhao & Shurong Sun & Zhenlai Han & Qiuping Li, 2011. "Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    2. Yige Zhao & Shurong Sun & Zhenlai Han & Qiuping Li, 2011. "Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-16, December.
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    Citations

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    Cited by:

    1. Zhaocai Hao & Yubo Huang, 2014. "Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Ruihui Huang, 2013. "Existence and Uniqueness of Solutions for a Fractional Order Antiperiodic Boundary Value Problem with a p‐Laplacian Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Zhang, Xinguang & Liu, Lishan & Wu, Yonghong & Wiwatanapataphee, B., 2015. "The spectral analysis for a singular fractional differential equation with a signed measure," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 252-263.
    4. Ge Dong, 2014. "Positive Solutions for the Eigenvalue Problem of Semipositone Fractional Order Differential Equation with Multipoint Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. 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).
    6. Ge Bin, 2012. "Multiple Solutions for a Class of Fractional Boundary Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. Min Jia & Xin Liu & Xuemai Gu, 2012. "Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional‐Order Integral Boundary Value Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    8. 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).
    9. Teng Ren & Xiaochun Chen, 2013. "Positive Solutions of Fractional Differential Equation with p‐Laplacian Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    10. 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).
    11. Rui Li & Haoqian Zhang & Hao Tao, 2013. "Unique Solution of a Coupled Fractional Differential System Involving Integral Boundary Conditions from Economic Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    12. 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).
    13. Xinguang Zhang & Cuiling Mao & Yonghong Wu & Hua Su, 2014. "Positive Solutions of a Singular Nonlocal Fractional Order Differential System via Schauder’s Fixed Point Theorem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    14. Jun-qi He & Xue-li Song, 2014. "The Uniqueness of Solution for a Class of Fractional Order Nonlinear Systems with p‐Laplacian Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    15. Jing Wu & Tunhua Wu, 2013. "A Sum Operator Method for the Existence and Uniqueness of Positive Solutions to a System of Nonlinear Fractional Integral Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    16. Yumei Zou & Lishan Liu & Yujun Cui, 2014. "The Existence of Solutions for Four‐Point Coupled Boundary Value Problems of Fractional Differential Equations at Resonance," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    17. Wenquan Wu & Xiangbing Zhou, 2013. "Eigenvalue of Fractional Differential Equations with -Laplacian Operator," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-8, March.
    18. Tunhua Wu & Xinguang Zhang & Yinan Lu, 2012. "Solutions of Sign‐Changing Fractional Differential Equation with the Fractional Derivatives," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    19. 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).
    20. Han, Zhenlai & Lu, Hongling & Zhang, Chao, 2015. "Positive solutions for eigenvalue problems of fractional differential equation with generalized p-Laplacian," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 526-536.
    21. Huichao Zou & Yonghong Fan, 2013. "Remark on Existence and Uniqueness of Solutions for a Coupled System of Multiterm Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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