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 $r \to 0$ and as $r \to \infty$. 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]

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

#### Abstract

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 $r \to 0$ and as $r \to \infty$. 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]
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2009
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/39375
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