Consider
y
=
f
(
t
,
y
,
y
′
)
y = f(t,y,y’)
with boundary conditions
(
0
,
y
(
0
)
,
y
′
(
0
)
)
∈
S
1
,
(
1
,
y
(
1
)
,
y
′
(
1
)
)
∈
S
2
(0,y(0),y’(0)) \in {S_1},(1,y(1),y’(1)) \in {S_2}
. It is shown that the boundary value problem has a solution for certain boundary sets
S
1
{S_1}
and
S
2
{S_2}
which depend on the assumed Nagumo condition for
f
(
t
,
y
,
y
′
)
f(t,y,y’)
.