@article{Wang2022, 
author = {Yanhua Wang and Min Liu and Gongming Wei},
title = {Existence of ground state for coupled system of biharmonic Schrödinger equations},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {3},
pages = {3719-3730},
keywords = {system of Schrödinger equations, ground state solution, Nehari manifold, concentration-compactness principle},
url = {https://www.sciopen.com/article/10.3934/math.2022206},
doi = {10.3934/math.2022206},
abstract = {In this paper we consider the following system of coupled biharmonic Schrödinger equations           {                                        Δ                          2                                u          +                      λ                          1                                u          =                      u                          3                                +          β          u                      v                          2                                ,                                                  Δ                          2                                v          +                      λ                          2                                v          =                      v                          3                                +          β                      u                          2                                v          ,                        where    (  u  ,  v  )  ∈      H          2        (                    R                    N        )  ×      H    2    (            R        N    ),    1  ≤  N  ≤  7,        λ          i        >  0  (  i  =  1  ,  2  ) and    β denotes a real coupling parameter. By Nehari manifold method and concentration compactness theorem, we prove the existence of ground state solution for the coupled system of Schrödinger equations. Previous results on ground state solutions are obtained in radially symmetric Sobolev space        H    r    2    (            R        N    )  ×      H    r    2    (            R        N    ). When    β satisfies some conditions, we prove the existence of ground state solution in the whole space        H    2    (            R        N    )  ×      H    2    (            R        N    ).}
}