Existence of solutions of scalar field equations with fractional operator

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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
Volume19
Issue number1
DOIs
Publication statusPublished - 2017 Mar 1
Externally publishedYes

Fingerprint

Scalar Field
Existence of Solutions
Fractional
Least Energy Solutions
Mountain Pass
Infinitely Many Solutions
Optimal Path
Existence of Positive Solutions
Operator
Nonlinearity
Energy

Keywords

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

ASJC Scopus subject areas

  • Modelling and Simulation
  • Geometry and Topology
  • Applied Mathematics

Cite this

Existence of solutions of scalar field equations with fractional operator. / Ikoma, Norihisa.

In: Journal of Fixed Point Theory and Applications, Vol. 19, No. 1, 01.03.2017, p. 649-690.

Research output: Contribution to journalArticle

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