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 -