Standing waves for the pseudo-relativistic Hartree equation with Berestycki-Lions nonlinearity

Abstract

We study the following class of pseudo-relativistic Hartree equations − ε 2 Δ + m 2 u + V ( x ) u = ε μ − N ( | x | − μ ⁎ F ( u ) ) f ( u ) in R N , where the nonlinearity satisfies general hypotheses of Berestycki-Lions type. By using the method of penalization arguments, we prove the existence of a family of localized positive solutions that concentrate at the local minimum points of the indefinite potential V ( x ) , as ε → 0 .