Concentration phenomena for a fractional relativistic Schrödinger equation with critical growth

In this paper, we are concerned with the following fractional relativistic Schr & ouml;dinger equation with critical growth: {(-Delta+m(2))su+V(epsilon x)u=f(u)+u(2 & lowast;)s(-1) in R-N,R- ( )u is an element of H-s(R-N),u>0 in R-N, where epsilon>0 is a small parameter, s is an element of(0,1), m>0, N>2s, 2(s)(& lowast;)=(2N)/(N-2s )is the fractional critical exponent, (-Delta+m(2))(s) is the fractional relativistic Schr & ouml;dinger operator, V:R-N -> R is a continuous potential, and f:R -> R 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(epsilon)is an element of H-s(R-N), with exponential decay, which concentrates around a local minimum of V as epsilon -> 0.