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
FRANCA, Matteo
2009-01-01
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]File in questo prodotto:
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