# On the complex structure of positive solutions to Matukuma-type equations

### Moxun Tang

Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA### Patricio Felmer

Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (CNRS UMI2807), Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile### Alexander Quaas

Departamento de Matemática, Universidad Técnica Santa María, Casilla V-110, Avda. España 1680, Valparaíso, Chile

## Abstract

In this article we consider the Matukuma type equation

for positive radially symmetric solutions. We assume that $N>2$, $p>1$ and $K(r)⩾0$, for all $r⩾0$. When $K$ satisfies some appropriate monotonicity assumption, the set of positive solutions of (0.1) is well understood. In this work we propose a constructive approach to start the analysis of the structure of the set of positive solutions when this monotonicity assumption fails. We construct some functions $K$ so that the equation exhibits a very complex structure. This function $K$ depends on a set of four parameters: $p$, $N$ and the limits at zero and infinity of certain quotient describing the growth of $K$.

## Cite this article

Moxun Tang, Patricio Felmer, Alexander Quaas, On the complex structure of positive solutions to Matukuma-type equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 3, pp. 869–887

DOI 10.1016/J.ANIHPC.2008.03.006