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Concentrating bounded states for fractional Schr\"{o}dinger-Poisson system. (arXiv:1710.03495v1 [math.AP])
来源于:arXiv
In this paper, we study the following fractional Schr\"{o}dinger-Poisson
system \begin{equation*} \left\{
\begin{array}{ll}
\varepsilon^{2s}(-\Delta)^su+V(x)u+\phi u=g(u) & \hbox{in $\mathbb{R}^3$,}
\varepsilon^{2t}(-\Delta)^t\phi=u^2,\,\, u>0& \hbox{in $\mathbb{R}^3$,}
\end{array} \right. \end{equation*} where $s,t\in(0,1)$, $\varepsilon>0$ is a
small parameter. Under some local assumptions on $V(x)$ and suitable
assumptions on the nonlinearity $g$, we construct a family of positive
solutions $u_{\varepsilon}\in H_{\varepsilon}$ which concentrates around the
global minima of $V(x)$ as $\varepsilon\rightarrow0$. 查看全文>>