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Positive solutions for a fractional boundary value problem with p-Laplacian operator

  • Applied mathematics
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Abstract

In this paper, we are mainly concerned with positive solutions for a p-Laplacian fractional boundary value problem. By virtue of Jensen’s inequalities and some new properties of the Green function of the problem, we adopt the Krasnoselskii-Zabreiko fixed point theorem to establish the results of existence and multiplicity of the positive solutions. Finally, a uniqueness theorem is established by using a fixed point theorem of concave operator and an example is given to illustrate the result.

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Authors and Affiliations

  1. Department of Mathematics, Shandong Jianzhu University, Jinan, Shandong, 250101, China

    Youzheng Ding & Zhongli Wei

  2. School of Mathematics, Shandong University, Jinan, Shandong, 250100, China

    Youzheng Ding, Zhongli Wei & Jiafa Xu

Authors
  1. Youzheng Ding
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  2. Zhongli Wei
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  3. Jiafa Xu
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Corresponding author

Correspondence to Youzheng Ding.

Additional information

Research supported by the NNSF-China (10971046), the NSF of Shandong Province (ZR2012AQ007) and Graduate Independent Innovation Foundation of Shandong University (yzc12063).

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Ding, Y., Wei, Z. & Xu, J. Positive solutions for a fractional boundary value problem with p-Laplacian operator. J. Appl. Math. Comput. 41, 257–268 (2013). https://doi.org/10.1007/s12190-012-0594-4

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  • DOI: https://doi.org/10.1007/s12190-012-0594-4

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