We show the existence of a dense subset
D
\mathcal {D}
of
C
(
R
)
\mathcal {C}(\mathbb {R})
such that, for
g
g
in it, the problem
\[
minimum
∫
0
T
g
(
x
(
t
)
)
d
t
+
∫
0
T
h
(
x
′
(
t
)
)
d
t
,
x
(
0
)
=
a
,
x
(
T
)
=
b
{\text {minimum}}\;\int _0^T {g(x(t))dt + \int _0^T {h(x’(t))dt,\;x(0) = a,\;x(T) = b} }
\]
admits a solution for every lower semicontinuous
h
h
satisfying growth conditions