CANONICAL FORM RELATED WITH RADIAL SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS AND ITS APPLICATIONS

Abstract

We explain that boundary value problems which satisfy radial solutions are reduced to a canonical form after a suitable change of variables. We introduce structure theorems to the canonical form to equations with power nonlinearities with the homogeneous Dirichlet boundary condition. By virtue of this fact, we can understand known results systematically, make clear unknown structure of various equations. As applications, we can investigate the structure of radial solutions including all solutions with singularity at r = 0 and r = 1 of Matukuma’s equation.