@article{Xiao2022, 
author = {Yingying Xiao and Chuanxi Zhu and Li Xie},
title = {Existence of ground state solutions for the modified Chern-Simons-Schrödinger equations with general Choquard type nonlinearity},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {4},
pages = {7166-7176},
keywords = {Chern-Simons-Schrödinger equations, ground state solutions, variational methods, monotone trick, general Choquard type},
url = {https://www.sciopen.com/article/10.3934/math.2022399},
doi = {10.3934/math.2022399},
abstract = {In this paper, we are concerned with the following modified Schrödinger equation                       −        Δ        u        +        V        (                  |                x                  |                )        u        −        κ        u        Δ        (                  u          2                )        +                                                    q                                            h              2                        (                          |                        x                          |                        )                                              |                        x                                          |                            2                                      (        1        +        κ                  u          2                )        u                +        q                  (                                    ∫                                                |                                x                                  |                                                            +                ∞                                                                    h                (                s                )                            s                        (            2            +            κ                          u              2                        (            s            )            )                          u              2                        (            s            )                                          d                                      s                    )                u        =        (                  I          α                ∗        F        (        u        )        )        f        (        u        )        ,                        x        ∈                                            R                                2                ,            where    κ,    q  >  0,        I    α   is a Riesz potential,    α  ∈  (  0  ,  2  ) and    V  ∈      C    (                    R              2    ,            R        ),    F  (  t  )  =      ∫    0    t    f  (  s  )            d        s. Under appropriate assumptions on    f and    V  (  x  ), by using the variational methods, we establish the existence of ground state solutions of the above equation.}
}