Title: Concentration phenomena for a fractional Schrödinger-Kirchhoff type equation,
Abstract: In this paper we deal with the multiplicity and concentration of positive
solutions for the following fractional Schrödinger-Kirchhoff type equation
\begin{equation*} M\left(\frac{1}{\varepsilon^{3-2s}}
\iint_{\mathbb{R}^{6}}\frac{|u(x)- u(y)|^{2}}{|x-y|^{3+2s}} dxdy +
\frac{1}{\varepsilon^{3}} \int_{\mathbb{R}^{3}} V(x)u^{2}
dx\right)[\varepsilon^{2s} (-\Delta)^{s}u+ V(x)u]= f(u) \, \mbox{in}
\mathbb{R}^{3} \end{equation*} where $\varepsilon>0$ is a small parameter,
$s\in (\frac{3}{4}, 1)$, $(-\Delta)^{s}$ is the fractional Laplacian, $M$ is a
Kirchhoff function, $V$ is a continuous positive potential and $f$ is a
superlinear continuous function with subcritical growth. By using penalization
techniques and Ljusternik-Schnirelmann theory, we investigate the relation
between the number of positive solutions with the topology of the set where the
potential attains its minimum.