Concentration of bound states for fractional Schrödinger-Poisson system via penalization methods (Q2128870)

This paper studies the following fractional Schrödinger-Poisson system \begin{align*} &\varepsilon^{2s}(-\Delta)^{s} u+V(x)u+\phi u=g(u),\,\,\text{in}\,\,\mathbb{R}^3,\\ &\varepsilon^{2t}(-\Delta)^t \phi=u^2,\,\,\text{in}\,\,\mathbb{R}^3, \end{align*} where \(s,\,t\in (0,\,1)\), \(\varepsilon>0\) is a small parameter. Assuming that \(V(x)>0\) achieves its minimum in a bounded domain and the nonlinearity \(g(u)\) is superlinear at zero and subcritical at infinity, this paper obtains a solution concentrating at the global minima of \(V(x)\). The main argument is based on a penalization methods.