Existence and multiplicity of sign-changing solutions for a Schrödinger-Bopp-Podolsky system - Wang, Lixiong; Chen, Haibo; Liu, Senli (Topological Methods in Nonlinear Analysis, 2022)
In this paper, we deal with the following Schrödinger-Bopp-Podolsky system:\begin{equation}\label{P1}\begin{cases}-\Delta u+u+\phi u=f(u),\\-\Delta\phi +\varepsilon^{2}\Delta^{2}\phi =4\pi u^{2},\end{cases}\tag{$\rom{P}_{\varepsilon}$}\quad \hbox{in }\mathbb{R}^{3},\end{equation}where $\varepsilon> 0$ and $f$ is a continuous, superlinear and subcritical nonlinearity.By using a perturbation approach and the method of invariant sets of descending flow incorporated with minimax arguments,we prove the existence and multiplicity of sign-changing solutionsof syste (P1).Moreover, the asymptotic behavior of sign-changing solutions is also established.Our results mainly extend the results in Liu, Wang and Zhang ([Liuzhaoli2016AMPA], Ann. Mat. Pura Appl. 2016).