@article{Cheng2022, 
author = {Kun Cheng and Li Wang},
title = {Nodal solutions for the Kirchhoff-Schrödinger-Poisson system in              R        3},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {9},
pages = {16787-16810},
keywords = {nodal solutions, Kirchhoff type problem, Schrödinger-Poisson system, variational methods, disc's theorem},
url = {https://www.sciopen.com/article/10.3934/math.2022922},
doi = {10.3934/math.2022922},
abstract = {This paper is dedicated to studying the following Kirchhoff-Schrödinger-Poisson system:         {                            −                      (                          a              +              b                              ∫                                                                            R                                        3                                                                              |                            ∇              u                                                |                                2                            d              x                        )                    Δ          u          +          V          (                      |                    x                      |                    )          u          +          λ          ϕ          u          =          K          (                      |                    x                      |                    )          f          (          u          )          ,                          x          ∈                                    R                                      3                                ,                                      −          Δ          ϕ          =                      u            2                    ,                          x          ∈                                    R                                      3                                ,                        where    V  ,  K are radial and bounded away from below by positive numbers. Under some weaker assumptions on the nonlinearity    f, we develop a direct approach to establish the existence of infinitely many nodal solutions    {      u    k          b      ,      λ        } with a prescribed number of nodes    k, by using the Gersgorin disc's theorem, Miranda theorem and Brouwer degree theory. Moreover, we prove that the energy of    {      u    k          b      ,      λ        } is strictly increasing in    k, and give a convergence property of    {      u    k          b      ,      λ        } as    b  →  0 and    λ  →  0.}
}