On existence and concentration of solutions for Hamiltonian systems involving fractional operator with critical exponential growth

This paper is concerned with the existence and concentration of ground state solutions for the following class of fractional Schrodinger system (-Delta)(1/2)u+(lambda a(x)+1)u=H-v(u,v)in R, u,v is an element of H-1/2(R), (-Delta)(1/2)v+(lambda a(x)+1)v=H-u(u,v)in R, u,v is an element of H-1/2(R), where H has exponential critical growth, lambda is a positive parameter and a(x) has a potential well with int(a(-1)(0)) consisting of k disjoint components Omega(1), ... Omega(k). The proof relies on variational methods and combines truncation arguments and the Moser iteration technique.