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Multiple Positive Solutions of Nonlinear Boundary Value Problem for Finite Fractional Difference

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Listed:
  • Yansheng He
  • Mingzhe Sun
  • Chengmin Hou

Abstract

We consider a discrete fractional nonlinear boundary value problem in which nonlinear term f is involved with the fractional order difference. And we transform the fractional boundary value problem into boundary value problem of integer order difference equation. By using a generalization of Leggett‐Williams fixed‐point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions.

Suggested Citation

  • Yansheng He & Mingzhe Sun & Chengmin Hou, 2014. "Multiple Positive Solutions of Nonlinear Boundary Value Problem for Finite Fractional Difference," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:147975
    DOI: 10.1155/2014/147975
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    References listed on IDEAS

    as
    1. Zuoshi Xie & Yuanfeng Jin & Chengmin Hou, 2012. "Multiple Solutions for a Fractional Difference Boundary Value Problem via Variational Approach," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, December.
    2. Ravi P. Agarwal & Donal O’Regan & Patricia J. Y. Wong, 1999. "Positive Solutions of Differential, Difference and Integral Equations," Springer Books, Springer, number 978-94-015-9171-3, March.
    3. Zuoshi Xie & Yuanfeng Jin & Chengmin Hou, 2012. "Multiple Solutions for a Fractional Difference Boundary Value Problem via Variational Approach," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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