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| In this paper, we study the following Schr\"{o}dinger-Poisson system \begin{align*} \begin{cases} -\Delta u+\lambda\phi u=g(u)+h(x), &\mathrm{in}\ \mathbb{R}^{3},\\ -\Delta \phi=u^2, & \mathrm{in}\ \mathbb{R}^{3}, \end{cases} \end{align*}where $\lambda >0$ is a parameter, $h(x) \not \equiv0$. Under the Berestycki-Lions type conditions, we prove that there exists $\lambda_{0}>0$ such that the system has at least two positive radial solutions for $\lambda\in(0,\lambda_{0})$ by using variational methods. |
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| Keywords:Partial differential equation; Nonhomogeneous Schr\"{o}dinger-Poisson system; Variational methods; Multiple positive solutions; Berestycki-Lions type conditions |
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