Funkcialaj Ekvacioj
Print ISSN : 0532-8721
Structure Theorems for Positive Radial Solutions of the Generalized Scalar Curvature Equation
Matteo Franca
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2009 Volume 52 Issue 3 Pages 343-369

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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 → 0 and as r → ∞. 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 [21] and [22].

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© 2009 by the Division of Functional Equations, The Mathematical Society of Japan
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