ABSTRACT
We next study global compactly supported solutions of ODE (40). For p ≤ n + 1, the local interface analysis from Section 4.3 applies to (40). Indeed, close to the interface point y = y0 > 0 of the similarity profile f(y), ODE (40) contains the same leading terms as in (27) and other linear two terms are negligible as y → y−0 . It is key that, taking into account the local result (31) and bearing in mind
the two boundary conditions in (42) or (43), we may expect that
there exists not more than a countable set {fk} of solutions. (45) These speculations assume a certain “analyticity” hypothesis concerning the dependence on parameters in the degenerate ODE (40), which is plausible but not easy to prove. Actually, this means that, relative to the parameter p > 1, we can expect at most a countable set of p-branches of solutions. To begin with, this is true for the linear case n = 0 and p = 1.
