LAUSR

Abstract In this paper, we study an elliptic equation arising from the self-dual Maxwell gauged O ( 3 ) sigma model coupled with gravity. When the parameter τ equals 1 and there is only one singular source, we consider radially symmetric solutions. There appear three important constants: a positive parameter a representing a scaled gravitational constant, a nonnegative integer N 1 representing the total string number, and a nonnegative integer N 2 representing the total anti-string number. The values of the products a N 1 , a N 2 ∈ [ 0 , ∞ ) play a crucial role in classifying radial solutions. By using the decay rates of solutions at infinity, we provide a complete classification of solutions for all possible values of a N 1 and a N 2 . This improves previously known results.