文章基本信息

标题：Existence of ground state solutions for an asymptotically 2-linear fractional Schrödinger–Poisson system
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作者：Dandan Yang ; Chuanzhi Bai
期刊名称：Boundary Value Problems
印刷版ISSN：1687-2762
电子版ISSN：1687-2770
出版年度：2020
卷号：2020
期号：1
页码：1-9
DOI：10.1186/s13661-019-01314-2
出版社：Hindawi Publishing Corporation
摘要：In this paper, we investigate the following fractional Schrödinger–Poisson system:$$\left \{ \textstyle\begin{array}{l@{\quad}l} (-\Delta)^{s} u + u + \phi u = f(u), & \text{in } \mathbb{R}^{3}, \\ (-\Delta)^{t} \phi= u^{2}, & \text{in } \mathbb{R}^{3}, \end{array}\displaystyle \right . $$ where $\frac{3}{4} < s < 1$, $\frac{1}{2} < t < 1$, and f is a continuous function, which is superlinear at zero, with $f(\tau) \tau \ge3 F(\tau) \ge0$, $F(\tau) = \int_{0}^{\tau} f(s) \,ds$, $\tau \in\mathbb{R}$. We prove that the system admits a ground state solution under the asymptotically 2-linear condition. The result here extends the existing study..
关键词：Fractional Schrödinger–Poisson system ; Ground state solution ; Asymptotically 2-linear ; Variational methods ;