@article{Tian2022, 
author = {Guaiqi Tian and Hongmin Suo and Yucheng An},
title = {Multiple positive solutions for a bi-nonlocal Kirchhoff-Schr                     o            ¨      dinger-Poisson system with critical growth},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {12},
pages = {4493-4506},
keywords = {Kirchhoff-Schrödinger-Poisson systems, positive solutions, critical growth, concentration compactness principle, multiplicity},
url = {https://www.sciopen.com/article/10.3934/era.2022228},
doi = {10.3934/era.2022228},
abstract = {In this article, we study the following bi-nonlocal Kirchhoff-Schr                     o            ¨      dinger-Poisson system with critical growth:         {                            −                                    (                                                ∫                                      Ω                                                                    |                                ∇                u                                                      |                                    2                                d                x                            )                        r                    Δ          u          +          ϕ          u          =                      u            5                    +          λ                                    (                                                ∫                                      Ω                                                  F                (                x                ,                u                )                d                x                            )                        s                    f          (          x          ,          u          )          ,                                      i            n                                        Ω          ,                                      −          Δ          ϕ          =                      u            2                    ,          u          >          0          ,                                      i            n                                        Ω          ,                                      u          =          ϕ          =          0          ,                                      o            n                                        ∂          Ω          ,                        where    Ω  ⊂            R        3   is a smooth bounded domain,    λ  >  0,    0  ≤  r  <  1,    0  <  s  <            1      −      r              3      (      r      +      1      )       and    f  (  x  ,  u  ) satisfies some suitable assumptions. By using the concentration compactness principle, the multiplicity of positive solutions for the above system is established.}
}