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Positive Solutions for Coupled Nonlinear Fractional Differential Equations

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  • Wenning Liu
  • Xingjie Yan
  • Wei Qi

Abstract

We consider the existence of positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary values. Assume the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing two cones K1, K2 and computing the fixed point index in product cone K1 × K2, we obtain that the system has a pair of positive solutions. It is remarkable that it is established on the Cartesian product of two cones, in which the feature of two equations can be opposite.

Suggested Citation

  • Wenning Liu & Xingjie Yan & Wei Qi, 2014. "Positive Solutions for Coupled Nonlinear Fractional Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:790862
    DOI: 10.1155/2014/790862
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    References listed on IDEAS

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    1. Jinhua Wang & Hongjun Xiang & Zhigang Liu, 2010. "Positive Solution to Nonzero Boundary Values Problem for a Coupled System of Nonlinear Fractional Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-12, July.
    2. Bashir Ahmad & Juan J. Nieto, 2009. "Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-9, July.
    3. Bashir Ahmad & Juan J. Nieto, 2009. "Existence of Solutions for Nonlocal Boundary Value Problems of Higher‐Order Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    4. 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).
    5. 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.
    6. Klaus Deimling, 1985. "Nonlinear Functional Analysis," Springer Books, Springer, number 978-3-662-00547-7, March.
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    Cited by:

    1. Ying Wang & Lishan Liu & Xinguang Zhang & Yonghong Wu, 2014. "Positive Solutions for (n − 1,1)‐Type Singular Fractional Differential System with Coupled Integral Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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