On fractional Schrödinger equations with Hartree type nonlinearities

Silvia Cingolani; Marco Gallo; Kazunaga Tanaka

doi:10.3934/mine.2022056

On fractional Schrödinger equations with Hartree type nonlinearities

Silvia Cingolani^*, Marco Gallo, Kazunaga Tanaka

^*Corresponding author for this work

School of Fundamental Science and Engineering

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

2 Citations (Scopus)

Abstract

Goal of this paper is to study the following doubly nonlocal equation (equation presented) in the case of general nonlinearities F 2 C1(R) of Berestycki-Lions type, when N ≥ 2 and μ > 0 is fixed. Here (-Δ)s, s ∈(0; 1), denotes the fractional Laplacian, while the Hartree-type term is given by convolution with the Riesz potential Iα, α 2 (0; N). We prove existence of ground states of (P). Furthermore we obtain regularity and asymptotic decay of general solutions, extending some results contained in [23, 61].

Original language	English
Pages (from-to)	1-33
Number of pages	33
Journal	Mathematics In Engineering
Volume	4
Issue number	6
DOIs	https://doi.org/10.3934/mine.2022056
Publication status	Published - 2022 Jan 1

Keywords

Asymptotic decay
Choquard nonlinearity
Double nonlocality
Fractional Laplacian
Hartree term
Nonlinear Schr odinger equation
Regularity
Symmetric solutions

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

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10.3934/mine.2022056

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@article{f090bc438aea410ab4e43cde83669f6b,

title = "On fractional Schr{\"o}dinger equations with Hartree type nonlinearities",

abstract = "Goal of this paper is to study the following doubly nonlocal equation (equation presented) in the case of general nonlinearities F 2 C1(R) of Berestycki-Lions type, when N ≥ 2 and μ > 0 is fixed. Here (-Δ)s, s ∈(0; 1), denotes the fractional Laplacian, while the Hartree-type term is given by convolution with the Riesz potential Iα, α 2 (0; N). We prove existence of ground states of (P). Furthermore we obtain regularity and asymptotic decay of general solutions, extending some results contained in [23, 61].",

keywords = "Asymptotic decay, Choquard nonlinearity, Double nonlocality, Fractional Laplacian, Hartree term, Nonlinear Schr odinger equation, Regularity, Symmetric solutions",

author = "Silvia Cingolani and Marco Gallo and Kazunaga Tanaka",

note = "Funding Information: The first and second authors are supported by PRIN 2017JPCAPN “Qualitative and quantitative aspects of nonlinear PDEs” and by INdAM-GNAMPA. The third author is supported in part by Grant-in-Aid for Scientific Research (19H00644, 18KK0073, 17H02855, 16K13771) of Japan Society for the Promotion of Science. Publisher Copyright: {\textcopyright} 2022 the Author(s).",

year = "2022",

month = jan,

day = "1",

doi = "10.3934/mine.2022056",

language = "English",

volume = "4",

pages = "1--33",

journal = "Mathematics In Engineering",

issn = "2640-3501",

publisher = "American Institute of Mathematical Sciences",

number = "6",

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TY - JOUR

T1 - On fractional Schrödinger equations with Hartree type nonlinearities

AU - Cingolani, Silvia

AU - Gallo, Marco

AU - Tanaka, Kazunaga

N1 - Funding Information: The first and second authors are supported by PRIN 2017JPCAPN “Qualitative and quantitative aspects of nonlinear PDEs” and by INdAM-GNAMPA. The third author is supported in part by Grant-in-Aid for Scientific Research (19H00644, 18KK0073, 17H02855, 16K13771) of Japan Society for the Promotion of Science. Publisher Copyright: © 2022 the Author(s).

PY - 2022/1/1

Y1 - 2022/1/1

N2 - Goal of this paper is to study the following doubly nonlocal equation (equation presented) in the case of general nonlinearities F 2 C1(R) of Berestycki-Lions type, when N ≥ 2 and μ > 0 is fixed. Here (-Δ)s, s ∈(0; 1), denotes the fractional Laplacian, while the Hartree-type term is given by convolution with the Riesz potential Iα, α 2 (0; N). We prove existence of ground states of (P). Furthermore we obtain regularity and asymptotic decay of general solutions, extending some results contained in [23, 61].

AB - Goal of this paper is to study the following doubly nonlocal equation (equation presented) in the case of general nonlinearities F 2 C1(R) of Berestycki-Lions type, when N ≥ 2 and μ > 0 is fixed. Here (-Δ)s, s ∈(0; 1), denotes the fractional Laplacian, while the Hartree-type term is given by convolution with the Riesz potential Iα, α 2 (0; N). We prove existence of ground states of (P). Furthermore we obtain regularity and asymptotic decay of general solutions, extending some results contained in [23, 61].

KW - Asymptotic decay

KW - Choquard nonlinearity

KW - Double nonlocality

KW - Fractional Laplacian

KW - Hartree term

KW - Nonlinear Schr odinger equation

KW - Regularity

KW - Symmetric solutions

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U2 - 10.3934/mine.2022056

DO - 10.3934/mine.2022056

M3 - Article

AN - SCOPUS:85122981826

SN - 2640-3501

VL - 4

SP - 1

EP - 33

JO - Mathematics In Engineering

JF - Mathematics In Engineering

IS - 6

ER -

On fractional Schrödinger equations with Hartree type nonlinearities

Abstract

Keywords

ASJC Scopus subject areas

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