@article{Jian2023, 
author = {Hui Jian and Shenghao Feng and Li Wang},
title = {Sign-changing solutions of critical quasilinear Kirchhoff-Schrödinger-Poisson system with logarithmic nonlinearity},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {4},
pages = {8580-8609},
keywords = {quasilinear Kirchhoff-Schrödinger-Poisson, critical problem, logarithmic nonlinearity},
url = {https://www.sciopen.com/article/10.3934/math.2023431},
doi = {10.3934/math.2023431},
abstract = {In the present paper, we study the following Kirchhoff-Schrödinger-Poisson system with logarithmic and critical nonlinearity:                                                                           {                                                                            −                                              (                                            a                      +                      b                                              ∫                        Ω                                                                    |                                            ∇                      u                                                                        |                                                2                                                                                              d                                                                    x                                              )                                            Δ                      u                      +                      V                      (                      x                      )                      u                      −                                              1                        2                                            u                      Δ                      (                                              u                        2                                            )                      +                      ϕ                      u                      =                      λ                                              |                                            u                                                                        |                                                                          q                          −                          2                                                                    u                      ln                      ⁡                                              |                                            u                                                                        |                                                2                                            +                                              |                                            u                                                                        |                                                4                                            u                      ,                                                              x                      ∈                      Ω                      ,                                                                                                  −                      Δ                      ϕ                      =                                              u                        2                                            ,                                                              x                      ∈                      Ω                      ,                                                                                                  u                      =                      ϕ                      =                      0                      ,                                                              x                      ∈                      ∂                      Ω                      ,                                                                                                                              where    λ  ,  b  >  0  ,  a  >      1    4    ,  4  <  q  <  6  ,     V  (  x  ) is a smooth potential function and    Ω is a bounded domain in              R        3   with Lipschitz boundary. Combining constraint variational method and perturbation method, we prove that the above problem has a least energy sign-changing solution        u    0   which has precisely two nodal domains. Moreover, we show that the energy of        u    0   is strictly larger than twice the ground state energy.}
}