@article{Chen2023, 
author = {Jianqing Chen and Qihua Ruan and Qian Zhang},
title = {Odd symmetry of ground state solutions for the Choquard system},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {8},
pages = {17603-17619},
keywords = {ground state solution, Choquard system, odd symmetry, nonlocal Brézis-Lieb lemma},
url = {https://www.sciopen.com/article/10.3934/math.2023898},
doi = {10.3934/math.2023898},
abstract = {This paper is dedicated to the following Choquard system:         {                                              −          Δ          u          +          u          =                                    2              p                                      p              +              q                                            (                                I            α                    ∗                      |                    v                                    |                        q                                )                                |                    u                                    |                                      p              −              2                                u          ,                                                        −          Δ          v          +          v          =                                    2              q                                      p              +              q                                            (                                I            α                    ∗                      |                    u                                    |                        p                                )                                |                    v                                    |                                      q              −              2                                v          ,                                              u          (          x          )          →          0          ,                              v          (          x          )          →          0                                          as                                          |                    x                      |                    →          ∞          ,                        where    N  ≥  1,    α  ∈  (  0  ,  N  ) and              N      +      α        N    <  p  ,    q  <      2    ∗    α  , in which        2    ∗    α   denotes              N      +      α              N      −      2       if    N  ≥  3 and        2    ∗    α    :=  ∞ if    N  =  1  ,    2.        I    α   is a Riesz potential. We obtain the odd symmetry of ground state solutions via a variant of Nehari constraint. Our results can be looked on as a partial generalization to results by Ghimenti and Schaftingen (Nodal solutions for the Choquard equation, J. Funct. Anal. 271 (2016), 107).}
}