Existence of solutions of scalar field equations with fractional operator

Norihisa Ikoma

doi:10.1007/s11784-016-0369-x

Existence of solutions of scalar field equations with fractional operator

Norihisa Ikoma

Research output: Contribution to journal › Article › peer-review

16 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 R^N 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 R^N is established under suitable conditions on f(x, s).

Original language	English
Pages (from-to)	649-690
Number of pages	42
Journal	Journal of Fixed Point Theory and Applications
Volume	19
Issue number	1
DOIs	https://doi.org/10.1007/s11784-016-0369-x
Publication status	Published - 2017 Mar 1
Externally published	Yes

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

Access to Document

10.1007/s11784-016-0369-x

Cite this

@article{6cbb411202ce4eb59b1239098e668545,

title = "Existence of solutions of scalar field equations with fractional operator",

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).",

keywords = "Mountian pass theorem, Symmetric mountain pass theorem, The Pohozaev identity, Variational method",

author = "Norihisa Ikoma",

note = "Publisher Copyright: {\textcopyright} 2016, Springer International Publishing.",

year = "2017",

month = mar,

day = "1",

doi = "10.1007/s11784-016-0369-x",

language = "English",

volume = "19",

pages = "649--690",

journal = "Journal of Fixed Point Theory and Applications",

issn = "1661-7738",

publisher = "Springer Science + Business Media",

number = "1",

}

TY - JOUR

T1 - Existence of solutions of scalar field equations with fractional operator

AU - Ikoma, Norihisa

PY - 2017/3/1

Y1 - 2017/3/1

N2 - 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).

AB - 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).

KW - Mountian pass theorem

KW - Symmetric mountain pass theorem

KW - The Pohozaev identity

KW - Variational method

UR - http://www.scopus.com/inward/record.url?scp=84995427031&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84995427031&partnerID=8YFLogxK

U2 - 10.1007/s11784-016-0369-x

DO - 10.1007/s11784-016-0369-x

M3 - Article

AN - SCOPUS:84995427031

SN - 1661-7738

VL - 19

SP - 649

EP - 690

JO - Journal of Fixed Point Theory and Applications

JF - Journal of Fixed Point Theory and Applications

IS - 1

ER -

Existence of solutions of scalar field equations with fractional operator

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this