@Article{JNMA-6-3,
author = {Tang, Ronghua and Hui, Guo and Wang, Tao},
title = {On Nodal Solutions of the Schrödinger-Poisson System with a Cubic Term},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2024},
volume = {6},
number = {3},
pages = {623--642},
abstract = {<p style="text-align: justify;">In this paper, we consider the following Schrödinger-Poisson system with a cubic term $$\begin{align*}\tag{0.1}\label{0.1} \begin{cases} -\Delta u+V(|x|)u+\lambda\phi u=|u|^2u \ \&nbsp; {\rm in} \ \&nbsp; \mathbb{R}^3,\\ -\Delta\phi=u^2 \ \ {\rm in} \&nbsp; \ \mathbb{R}^3,&nbsp;\end{cases} \end{align*}$$&nbsp;where $λ &gt; 0$ and the radial function $V (x)$ is an external potential. By taking
advantage of the Gersgorin disc theorem and Miranda theorem, via the variational method and blow up analysis, we prove that for each positive integer $k,$ problem (0.1) admits a radial nodal solution $U^λ_{k,4}$ that changes sign exactly $k$ times. Furthermore, the energy of $U^λ_{k,4}$ is strictly increasing in $k$ and the
asymptotic behavior of $U^λ_{k,4}$ as $λ → 0_+$ is established. These results extend
the existing ones from the super-cubic case in [17] to the cubic case.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2024.623},
url = {https://global-sci.com/article/91172/on-nodal-solutions-of-the-schrodinger-poisson-system-with-a-cubic-term}
}