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 (- ) s u + V ( x) u = e mu- N 1 | x| mu * F( u) f ( u) in RN, where e > 0 is a parameter, s. ( 0, 1), N > 2s, (- ) s is the fractional Laplacian, V is a positive continuous potential with local minimum, 0 < mu < 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.