Existence and concentration of ground state solutions for a critical nonlocal Schrodinger equation in R2

We study the following singularly perturbed nonlocal Schrodinger equation -epsilon(2)Delta u + V(x)u = epsilon(mu-2)[1/vertical bar x vertical bar(mu) * F(u)]f(u) in R-2, where V(x) is a continuous real function on R-2, F (s) is the primitive of f (s), 0 < mu < 2 and s is a positive parameter. Assuming that the nonlinearity f (s) has critical exponential growth in the sense of Trudinger-Moser, we establish the existence and concentration of solutions by variational methods. (C) 2016 Elsevier Inc. All rights reserved.