Multiplicity and Concentration Results for a Fractional Choquard Equation via Penalization Method

This paper is devoted to the study of the following fractional Choquard equation $$ e^{2s}(-Delta)^{s} u + V(x)u = e^{mu-N}left(rac{1}{|x|^{mu}}*F(u) ight)f(u) mbox{ in } R^{N}, $$ where $arepsilon>0$ is a parameter, $sin (0, 1)$, $N>2s$, $(-Delta)^{s}$ is the fractional Laplacian, $V$ is a positive continuous potential with local minimum, $0<2s$, and $f$ is a superlinear continuous function with subcritical growth. By using the penalization method and the Ljusternik-Schnirelmann theory, we investigate the multiplicity and concentration of positive solutions for the above problem.