@article{Ouyang2023, 
author = {Kexin Ouyang and Yu Wei and Huiqin Lu},
title = {Positive ground state solutions for a class of fractional coupled Choquard systems},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {7},
pages = {15789-15804},
keywords = {fractional Choquard systems, ground state solution, asymptotic behaviour},
url = {https://www.sciopen.com/article/10.3934/math.2023806},
doi = {10.3934/math.2023806},
abstract = {In this paper, we combine the critical point theory and variational method to investigate the following a class of coupled fractional systems of Choquard type         {                            (          −          Δ                      )                          s                                u          +                      λ                          1                                u                          =          (                      I                          α                                ∗                      |                    u                                    |                                      p                                )                      |                    u                                    |                                      p              −              2                                u          +          β          v                                            in                                                                R                                      N                                ,                    (          −          Δ                      )                          s                                v          +                      λ                          2                                v                          =          (                      I                          α                                ∗                      |                    v                                    |                                      p                                )                      |                    v                                    |                                      p              −              2                                v          +          β          u                                            in                                              R                                      N                                ,                        with    s  ∈  (  0  ,  1  )  ,    N  ≥  3  ,    α  ∈  (  0  ,  N  )  ,    p  >  1,        λ          i        >  0 are constants for    i  =  1  ,    2,    β  >  0 is a parameter, and        I          α        (  x  ) is the Riesz Potential. We prove the existence and asymptotic behaviour of positive ground state solutions of the systems by using constrained minimization method and Hardy-Littlewood-Sobolev inequality. Moreover, nonexistence of nontrivial solutions is also obtained.}
}