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Concentration of bound states for fractional Schr��dinger-Poisson system via penalization methods
- Publication Year :
- 2017
- Publisher :
- arXiv, 2017.
-
Abstract
- In this paper, we study the following fractional Schr��dinger-Poisson system \begin{equation*} \left\{ \begin{array}{ll} \varepsilon^{2s}(-��)^su+V(x)u+��u=g(u) & \hbox{in $\mathbb{R}^3$,} \varepsilon^{2t}(-��)^t��=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 $\varepsilon\rightarrow0$.
- Subjects :
- FOS: Mathematics
35B38, 35R11
Analysis of PDEs (math.AP)
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi...........f83830798a293d794a05214a985f04ea
- Full Text :
- https://doi.org/10.48550/arxiv.1710.03495