Abstract

In this article we consider the Matukuma type equation(0.1)? u + K (r) up = 0 in RN 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. © 2008 Elsevier Masson SAS. All rights reserved.