Here we show the proofs alluded to in the section on analyzing
, after the balancing transformation.
Theorem 4.7.5 of [4, p. 188] asserts that if is a
narrowing antifunnel for the differential equation , and if
there is a function such that
,
in U,
and such that , then there is a unique
solution remaining in U as .
Applied to equation (12), we find
for t > 0, so with ,
the uniqueness criterion is satisfied. This shows that there is a unique
solution remaining in each antifunnel.