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Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator

  • Hongling Lu
  • Zhenlai HanEmail author
  • Chao Zhang
  • Yan Zhao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9045)

Abstract

In this paper, we deal with the following p-Laplacian fractional boundary value problem: \( \phi _p(D_{0+}^\alpha u(t))+f(t,u(t))=0,~0<t<1\), \(u(0)=u'(0)=u'(1)=0, \ \) where \(2<\alpha \leqslant 3\) is a real number. \(D_{0+}^\alpha \) is the standard Riemann–Liouville differentiation, and \(f:[0,1]\times [0,+\infty )\rightarrow [0,+\infty )\) is continuous. By the properties of the Green function and some fixed-point theorems on cone, some existence and multiplicity results of positive solutions are obtained. As applications, examples are presented to illustrate the main results.

Keywords

Fractional differential equation Boundary value problem P-Laplacian operator Green’s function Fixed-point theorem 

Notes

Acknowledgements

Corresponding author: Zhenlai Han. This research is supported by the Natural Science Foundation of China (61374074), Natural Science Outstanding Youth Foundation of Shandong Province (JQ201119) and supported by Shandong Provincial Natural Science Foundation (ZR2012AM009, ZR2013AL003).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Hongling Lu
    • 1
  • Zhenlai Han
    • 1
    Email author
  • Chao Zhang
    • 1
  • Yan Zhao
    • 1
  1. 1.School of Mathematical SciencesUniversity of JinanJinanPeople’s Republic of China

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