Canonical form related with radial solutions of semilinear elliptic equations and its applications

We explain that boundary value problems which satisfy radial solutions are reduced to a canonical form after a suitable change of variables. We introd uce structure theorems to the canonical form to equations with power nonlin earities with the homogeneous Dirichlet boundary condition. By virtue of th is fact, we can understand known results systematically, make clear unknown structure of various equations. As applications, we can investigate the structure of radial solutions inclu ding all solutions with singularity at r = 0 and r = infinity of Matukuma's equation.