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Multiple Solutions for a Fractional Difference Boundary Value Problem via Variational Approach

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  • Zuoshi Xie
  • Yuanfeng Jin
  • Chengmin Hou

Abstract

By establishing the corresponding variational framework and using the mountain pass theorem, linking theorem, and Clark theorem in critical point theory, we give the existence of multiple solutions for a fractional difference boundary value problem with parameter. Under some suitable assumptions, we obtain some results which ensure the existence of a well precise interval of parameter for which the problem admits multiple solutions. Some examples are presented to illustrate the main results.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlaaa:143914
    DOI: 10.1155/2012/143914
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