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. - In: FUNKCIALAJ EKVACIOJ. - ISSN 0532-8721. - STAMPA. - 52:3(2009), pp. 343-369. [10.1619/fesi.52.343]
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]I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
