Existence and multiplicity of sign-changing solutions for a Schrödinger-Bopp-Podolsky system
DOI:
https://doi.org/10.12775/TMNA.2021.045Keywords
Schrödinger-Bopp-Podolsky system, Sign-changing solutions, Perturbation approach, Invariant sets of descending flow, Asymptotic behaviorAbstract
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 solutions of 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).References
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