@article{Su2023, 
author = {Xia Su and Wen Guan and Xia Li},
title = {Least energy sign-changing solutions for Kirchhoff-Schrödinger-Poisson system on bounded domains},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {5},
pages = {2959-2973},
keywords = {Kirchhoff type equation, Schrödinger-Poisson problem, sign-changing solutions, Nehari manifold, the growth conditions},
url = {https://www.sciopen.com/article/10.3934/era.2023149},
doi = {10.3934/era.2023149},
abstract = {We investigate the following nonlinear system         {                            −          (          a          +          b                      ∫                          Ω                                            |                    ∇          u                                    |                                      2                                d          x          )          Δ          u          +          ϕ          u          =          λ          u          +          μ                      |                    u                                    |                                      2                                u          ,                              x          ∈          Ω          ,                                      −          Δ          ϕ          =                      u                          2                                ,                              x          ∈          Ω          ,                                      u          =          ϕ          =          0          ,                              x          ∈          ∂          Ω          ,                        with    a  ,  b  >  0,    λ  ,  μ  ∈      R  , and    Ω  ⊂            R              3       is bounded with smooth boundary. Let        λ          1        >  0 be the first eigenvalue of    (  −  Δ  u  ,      H          0              1        (  Ω  )  ). We get that for certain              μ      ~        >  0 there exists at least one least energy sign-changing solution for the above system if    λ  <  a      λ          1       and    μ  >            μ      ~      . In addition, we remark that the nonlinearity    λ  u  +  μ      |    u            |              2        u does not satisfy the growth conditions.}
}