(a) Suppose that
is a continuous solution of
,
,
where
are continuous and
for
. Show that
,
.
This I have done! But then we have...
(b) Moreover, if
is increasing for
, show that
,
.
In order to do the exercise, we are given as a theorem the following formulation of the Gronwall inequality:
If
,
,
where
,
for all
and
is continuous, and
is a continuous solution, then
,
.
However, I believe this theorem may only be useful for part (a), which, as I said, I have already done. I provide it just in case.
Thanks in advance!