On the multiplicity and concentration of positive solutions for a [formula omitted]-fractional Choquard equation in [formula omitted

Abstract

In this paper we deal with the following fractional Choquard equation εsp(−Δ)psu+V(x)|u|p−2u=εμ−N1|x|μ∗F(u)f(u)inRN,u∈Ws,p(RN),u>0inRN,where ε>0 is a small parameter, s∈(0,1), p∈(1,∞), N>sp, (−Δ)ps is the fractional p-Laplacian, V is a positive continuous potential, 0<μ<sp, and f is a continuous superlinear function with subcritical growth. Using minimax arguments and the Ljusternik–Schnirelmann category theory, we obtain the existence, multiplicity and concentration of positive solutions for ε>0 small enough.