In this paper, a system of semilinear elliptic equations arising from a relativistic
self-dual Maxwell-Chern-Simons O(3) sigma model is considered. We reveal the
uniqueness aspect of the topological solutions for the model. The uniqueness result
is associated with a clear solution structure of the equations of the radially symmetric
case. We locate each solution set denoted by a planar diagram. Published by AIP
We deal with a stationary problem of a reaction–diffusion system with a conservation law under the Neu-mann boundary condition. It is shown that the stationary problem turns to be the Euler–Lagrange equation of an energy functional with a mass constraint. When the domain is the finite interval (0, 1), we investigate the asymptotic profile of a strictly monotone minimizer of the energy as d, the ratio of the diffusion coef-ficient of the system, tends to zero. In view of a logarithmic function in the leading term of the potential, we get to a scaling parameter κsatisfying the relation ε:=√d=√logκ/κ2. The main result shows that a sequence of minimizers converges to a Dirac mass multiplied by the total mass and that by a scaling with κthe asymptotic profile exhibits a parabola in the nonvanishing region. We also prove the existence of an unstable monotone solution when the mass is small.