In this article we consider the Matukuma type equation
for positive radially symmetric solutions. We assume that , and , for all . 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. 869–887DOI 10.1016/J.ANIHPC.2008.03.006