@article{Cingolani2022, 
author = {Silvia Cingolani and Marco Gallo and Kazunaga Tanaka},
title = {On fractional Schrödinger equations with Hartree type nonlinearities},
year = {2022},
journal = {Mathematics in Engineering},
volume = {4},
number = {6},
pages = {1-33},
keywords = {nonlinear Schrödinger equation, double nonlocality, fractional Laplacian, Choquard nonlinearity, Hartree term, symmetric solutions, regularity, asymptotic decay},
url = {https://www.sciopen.com/article/10.3934/mine.2022056},
doi = {10.3934/mine.2022056},
abstract = {Goal of this paper is to study the following doubly nonlocal equation     (  −  Δ      )    s    u  +  μ  u  =  (      I    α    ∗  F  (  u  )  )      F    ′    (  u  )              i      n                            R            N                (            P        )in the case of general nonlinearities    F  ∈      C    1    (      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        I          α      ,    α  ∈  (  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].}
}