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The Positive Solutions for Integral Boundary Value Problem of Fractional p-Laplacian Equation with Mixed Derivatives

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Abstract

In this paper, we consider a class of integral boundary value problems of fractional p-Laplacian equation, which involve both Riemann–Liouville fractional derivative and Caputo fractional derivative. By using the generalization of Leggett–Williams fixed point theorem, some new results on the existence of at least three positive solutions to the boundary value problems are obtained. Finally, some examples are presented to illustrate the extensive potential applications of our main results.

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Author information

Correspondence to Xiping Liu.

Additional information

This work is supported by the National Natural Science Foundation of China (No. 11171220).

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Liu, X., Jia, M. The Positive Solutions for Integral Boundary Value Problem of Fractional p-Laplacian Equation with Mixed Derivatives. Mediterr. J. Math. 14, 94 (2017). https://doi.org/10.1007/s00009-017-0895-9

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Keywords

  • Fractional p-Laplacian equation
  • integral boundary value problem
  • positive solution
  • mixed derivatives
  • fixed point theorem

Mathematics Subject Classification

  • 34B10
  • 34B18
  • 26A33