Existence of solutions for
x
=
f
(
t
,
x
,
x
′
)
,
x
(
0
)
=
x
(
1
)
,
x
′
(
0
)
=
x
′
(
1
)
x = f(t,x,x’),x(0) = x(1),x’(0) = x’(1)
are proven by considering a simple alternative problem to which Leray-Schauder degree arguments can be directly applied.