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.