@article{Zhang2024, 
author = {Xinyi Zhang and Jian Zhang},
title = {On Schrödinger-Poisson equations with a critical nonlocal term},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {11122-11138},
keywords = {Schrödinger-Poisson equation, critical nonlocal term, critical nonlinearity, variational method},
url = {https://www.sciopen.com/article/10.3934/math.2024545},
doi = {10.3934/math.2024545},
abstract = {In this paper, we study the following non-autonomous Schrödinger-Poisson equation with a critical nonlocal term and a critical nonlinearity:         {                                              −          Δ          u          +          V          (          x          )          u          +          λ          ϕ                      |                    u                                    |                        3                    u          =          f          (          u          )          +          (                      u            +                                )            5                    ,                                          i            n                                                                                      R                        3                    ,                                                        −          Δ          ϕ          =                      |                    u                                    |                        5                    ,                                          i            n                                                                                      R                        3                    .                        First, we consider the case that the nonlinearity satisfies the Berestycki-Lions type condition with critical growth. Second, we consider the case that        i    n    t        V          −      1        (  0  ) is contained in a spherical shell. By using variational methods, we obtain the existence and asymptotic behavior of positive solutions.}
}