JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (12): 45-51.doi: 10.6040/j.issn.1671-9352.0.2021.058

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Existence of nontrivial weak solutions for fractional boundary value problems with variable coefficients

XUE Ting-ting, XU Yan, LIU Xiao-ping   

  1. School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830000, Xinjiang, China
  • Published:2021-11-25

Abstract: The existence of nontrivial weak solutions for a class of fractional Dirichlet boundary value problems with variable coefficients is studied by using Linking theorem and Mountain pass theorem. Under the variational framework, Ambrosetti-Rabinowtiz condition is mostly needed for the study of such problems, and the weaker condition than Ambrosetti-Rabinowtiz condition is given.

Key words: fractional differential equation, variable coefficient, weak solution, variational method

CLC Number: 

  • O175.14
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