MR2589660 Matteo FRANCA Matteo FRANCA Structure Theorems for Positive Radial Solutions of the Generalized Scalar Curvature Equation Funkcialaj Ekvacioj. Serio Internacia 52 2009 343--369 http://fe.math.kobe-u.ac.jp/FE/FullPapers/52-3/52_343.pdf http://www.ams.org/mathscinet-getitem?mr=MR2589660 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 $r\to0$ and as $r\to\infty$. The results are new even when $p=2$, that is when we consider the usual Laplacian.<br />     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 [21] and [22]. $p$-Laplace equations, Radial solution, Regular/singular ground state, Fowler inversion, Invariant manifold. 35J70, 35J10, 37D10. 52-343 2009 Structure Theorems for Positive Radial Solutions of the Generalized Scalar Curvature Equation Matteo FRANCA Matteo FRANCA
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