@article{Yang2023, 
author = {Chen Yang and Chun-Lei Tang},
title = {Sign-changing solutions for the Schrödinger-Poisson system with concave-convex nonlinearities in  R3},
year = {2023},
journal = {Communications in Analysis and Mechanics},
volume = {15},
number = {4},
pages = {638-657},
keywords = {variational method, Schrödinger-Poisson system, sign-changing solutions, concave-convex nonlinearities},
url = {https://www.sciopen.com/article/10.3934/cam.2023032},
doi = {10.3934/cam.2023032},
abstract = {In this paper, we consider the following Schrödinger-Poisson system   {−Δu+V(x)u+ϕu=|u|p−2u+λK(x)|u|q−2uinR3,−Δϕ=u2inR3.Under the weakly coercive assumption on  V and an appropriate condition on  K, we investigate the cases when the nonlinearities are of concave-convex type, that is,  1<q<2 and  4<p<6. By constructing a nonempty closed subset of the sign-changing Nehari manifold, we establish the existence of least energy sign-changing solutions provided that  λ∈(−∞,λ∗), where  λ∗>0 is a constant.}
}