Concentration phenomena for a fractional relativistic Schrödinger equation with critical growth

In this paper, we are concerned with the following fractional relativistic Schrödinger equation with critical growth: δ m u V u f u u-u H u in , , 0 in , s N s N N 2 2 1 s where 0 is a small parameter, s (0, 1), m 0, N 2s, =-2 s N N s 2 2 is the fractional critical exponent, (-δ + m2)s is the fractional relativistic Schrödinger operator, V : N → is a continuous potential, and f : → is a superlinear continuous nonlinearity with subcritical growth at infinity. Under suitable assumptions on the potential V, we construct a family of positive solutions u H N , with exponential decay, which concentrates around a local minimum of V as → 0.