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


In this article we consider the Matukuma type equation

for positive radially symmetric solutions. We assume that , and , for all . When 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 so that the equation exhibits a very complex structure. This function depends on a set of four parameters: , and the limits at zero and infinity of certain quotient describing the growth of .

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