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Putnam
1967 Putnam
A4
A4
Part of
1967 Putnam
Problems
(1)
Putnam 1967 A4
Source: Putnam 1967
5/13/2022
Show that if
λ
>
1
2
\lambda > \frac{1}{2}
λ
>
2
1
there does not exist a real-valued function
u
(
x
)
u(x)
u
(
x
)
such that for all
x
x
x
in the closed interval
[
0
,
1
]
[0,1]
[
0
,
1
]
the following holds:
u
(
x
)
=
1
+
λ
∫
x
1
u
(
y
)
u
(
y
−
x
)
d
y
.
u(x)= 1+ \lambda \int_{x}^{1} u(y) u(y-x) \; dy.
u
(
x
)
=
1
+
λ
∫
x
1
u
(
y
)
u
(
y
−
x
)
d
y
.
Putnam
function
Integral
functional equation