Structure Theorems for Positive Radial Solutions of the Generalized Scalar Curvature Equation

In this paper we analyze radial solutions for the generalized scalar curvature equation. In particular we prove the existence of ground states and singular ground states when the curvature $K(r)$ is monotone as $r o 0$ and as $r o infty$. The results are new even when $p=2$, that is when we consider the usual Laplacian. The proofs use a new Fowler transform which allow us to consider a 2-dimensional dynamical system thus giving a geometrical point of view on the problem. A key role in the analysis is played by an energy function which is a dynamical interpretation of the Pohozaev function used in [20,21]