Classification of solutions of elliptic equations arising from a gravitational O(3) gauge field model

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 tau equals 1 and there is only one singular source, we consider radially symmetric solutions. There appear three important constants: a positive parameter arepresenting a scaled gravitational constant, anonnegative 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 aN(1), aN(2) is an element of [0, infinity) 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 aN(1) and aN(2). This improves previously known results.