Concentration phenomena for the fractional relativistic Schrödinger–Choquard equation

Abstract

We consider the fractional relativistic Schrödinger–Choquard equation [Formula: see text] where [Formula: see text] is a small parameter, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] is the fractional relativistic Schrödinger operator, [Formula: see text] is a continuous potential having a local minimum, [Formula: see text] is a continuous nonlinearity with subcritical growth at infinity and [Formula: see text]. Exploiting appropriate variational arguments, we construct a family of solutions concentrating around the local minimum of [Formula: see text] as [Formula: see text].