MathDB

Putnam 1967 A4

Source: Putnam 1967

May 13, 2022

PutnamfunctionIntegralfunctional equation

Problem Statement

Show that if

\lambda > \frac{1}{2}

there does not exist a real-valued function

u(x)

such that for all

x

in the closed interval

[0,1]

the following holds:

u(x)= 1+ \lambda \int_{x}^{1} u(y) u(y-x) \; dy.

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