This paper deals with explicit formulas to the radial solutions of Liouville type semilinear elliptic partial differential equations and studies the corresponding Dirichlet problem with constant boundary data in a circle and in an annulus. It is concerned with the equations of two dimensional minimal surfaces in \( {\mathbf R}^{3} \) and \( {\mathbf R}^{4} \), the mean-field equation and others. Due to the exponential nonlinearity, the solutions can develop logarithmic singularities.