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Fractional Calculus and Applied Analysis

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Volume 18, Issue 1


Existence and Multiplicity of Solutions for Nonlinear Elliptic Problems with the Fractional Laplacian

Qing-Mei Zhou / Ke-Qi Wang
  • College of Mechanical and Electrical Engineering Northeast Forestry University Harbin, Heilongjiang, 150040, P. R.CHINA
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Published Online: 2015-02-10 | DOI: https://doi.org/10.1515/fca-2015-0009


In this paper we consider a nonlinear eigenvalue problem driven by the fractional Laplacian. By applying a version of the three-critical-points theorem we obtain the existence of three solutions of the problem in Hα(Ω). In addition the existence of at least two nontrivial solutions are also been obtained when 2<μ<2α*.

MSC 2010: 35J60; 47J30

Key Words and Phrases: fractional Laplacian; three critical points theorem; fractional Sobolev spaces; Dirichlet problem


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About the article

Received: 2014-04-30

Published Online: 2015-02-10

Citation Information: Fractional Calculus and Applied Analysis, Volume 18, Issue 1, Pages 133–145, ISSN (Online) 1314-2224, DOI: https://doi.org/10.1515/fca-2015-0009.

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