Uniqueness and solution structure of nonlinear equations arising from the Chern–Simons gauged O(3)O(3) sigma models

In this paper, we study radially symmetric solutions of nonlinear equations arising from the Chern–Simons gauged O(3)O(3) sigma models. There are three types of solutions according to the boundary conditions: topological solutions, nontopological solutions of type I and II. We classify radially symmetric nontopological solutions of type I and II by the decay rates β at infinity. In particular, we provide a complete picture of the graph of β, which gives uniqueness and structure of solutions.