Let us consider the following equation
for and
. In this entry, by using boothstrap argument, we show that
Theorem. If positive function
solves the equation, then
.
In the process of proving the result, we need the following result
Proposition. Let
be a non-negative function and set
.
For
, there exist positive constants
and
depending only on
and
such that for any
with
,
and
satisfying
we have
.