MathDB

Let

a(x)

and

b(x)

be continuous functions on

[0,1]

and let

0 \leq a(x) \leq a <1

on that range. Under what other conditions (if any) is the solution of the equation for

u,

u= \max_{0 \leq x \leq 1} b(x) +a(x)u

given by

u = \max_{0 \leq x \leq 1} \frac{b(x)}{1-a(x)}.

Problem Statement