Existence of solutions of scalar field equations with fractional operator

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16 Citations (Scopus)


In this paper, the existence of least energy solution and infinitely many solutions is proved for the equation (1 - Δ) αu= f(u) in RN where 0 < α< 1 , N≥ 2 and f(s) is a Berestycki–Lions type nonlinearity. The characterization of the least energy by the mountain pass value is also considered and the existence of optimal path is shown. Finally, exploiting these results, the existence of positive solution for the equation (1 - Δ) αu= f(x, u) in RN is established under suitable conditions on f(x, s).

Original languageEnglish
Pages (from-to)649-690
Number of pages42
JournalJournal of Fixed Point Theory and Applications
Issue number1
Publication statusPublished - 2017 Mar 1
Externally publishedYes


  • Mountian pass theorem
  • Symmetric mountain pass theorem
  • The Pohozaev identity
  • Variational method

ASJC Scopus subject areas

  • Modelling and Simulation
  • Geometry and Topology
  • Applied Mathematics


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