Solitons of the two-dimensional 3-component gauged sigma model (Q1284427)

The paper deals with the following boundary value problem arising from field theory (P): \[ u''+{1\over r} u'-\left({m^2(1-v)^2 \over r^2}+p \right)\sin u\cos u=0\text{ for }r>0, \] \[ v''-{1\over r} v'+2(1-v) \sin^2u=0 \text{ for }r>0, \] \[ u(0)= v(0)=v'(\infty)=0,\;u(\infty)=\pi,\quad u'>0,\;v'>0,\;v<1\text{ for }r>0. \] The main result is the following theorem: 1) For every \(m>0\), if \(p\geq 4m\), there is no solution to \((P)\). 2) For every \(m>0\), there exists \(p^*=p^* (m)>0\) such that for every \(p\in(0,p^*)\), there exists at least one solution to \((P)\). In addition, when \(m>1\), a lower bound for \(p^*(m)\) is given. The existence part of the theorem is proved by a shooting argument.