  This paper is concerned with the structure of the solutions to subcritical
elliptic equations related to the Matukuma equation. In certain cases the
complete structure of the solution set is known, and is comparable to that of
the original Matukuma equation. Here we derive sufficient conditions for a more
complicated solution set consisting of; (i) crossing solutions for small
initial conditions and large initial conditions; (ii) at least one open
interval of slowly decaying solutions; and (iii) at least two rapidly decaying
solutions. As a consequence we obtain multiplicity results for rapidly
decaying, or minimal solutions.
