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 -