  This paper is motivated by a gauged Schrodinger equation in dimension 2
including the so-called Chern-Simons term. The radially symmetric case leads to
an elliptic problem with a nonlocal defocusing term, in competition with a
local focusing nonlinearity. In this work we pose the equations in a ball under
homogeneous Dirichlet boundary conditions. By using singular perturbation
arguments we prove existence of solutions for large values of the radius. Those
solutions are located close to the boundary and the limit profile is given.
