Existence and concentration of ground state solutions for a critical nonlocal Schrödinger equation in [formula omitted

Abstract

We study the following singularly perturbed nonlocal Schrödinger equation−ε2Δu+V(x)u=εμ−2[1|x|μ⁎F(u)]f(u)inR2, where V(x) is a continuous real function on R2, F(s) is the primitive of f(s), 0<μ<2 and ε 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.