  This paper will discuss a class of semilinear partial differential equations
induced by studying the limiting behaviour of Hermitian Yang-Mills metrics. We
will study the radial symmetry of the $C^{2}$ global solution of this equation
in $\mathbb{R}^{2}$ and the existence of $C^{2,\alpha}$ solution of the
Dirichlet boundary value problem in any bounded domain.
