Uniqueness and solution structure of nonlinear equations arising from the Chern-Simons gauged \(O(3)\) sigma models (Q2434672)

There exist three types of solutions of nonlinear equations arising from the Chern-Simons gauged \(O(3)\) sigma models, according to the boundary conditions: topological solutions, and nontopological solutions of type I and II. The authors classify the radially symmetric nontopological solutions of type I and II via shooting parameters and decay rates of \(\beta\) at infinity and provide, in particular, a complete picture of the graph of \(\beta\), which gives uniqueness or multiplicities of solutions.