We study
ε
2
u
¨
=
f
(
u
,
x
)
=
A
u
(
1
−
u
)
(
ϕ
−
u
)
\varepsilon ^2\ddot {u}=f(u,x)=A\, u\, (1-u)\,(\phi -u)
, where
A
=
A
(
u
,
x
)
>
0
A=A(u,x)>0
,
ϕ
=
ϕ
(
x
)
∈
(
0
,
1
)
\phi =\phi (x)\in (0,1)
, and
ε
>
0
\varepsilon >0
is sufficiently small, on an interval
[
0
,
L
]
[0,L]
with boundary conditions
u
˙
=
0
\dot {u}=0
at
x
=
0
,
L
x=0,L
. All solutions with an
ε
\varepsilon
independent number of oscillations are analyzed. Existence of complicated patterns of layers and spikes is proved, and their Morse index is determined. It is observed that the results extend to
f
=
A
(
u
,
x
)
(
u
−
ϕ
−
)
(
u
−
ϕ
)
(
u
−
ϕ
+
)
f=A(u,x)\; (u-\phi _-)\,(u-\phi )\,(u-\phi _+)
with
ϕ
−
(
x
)
>
ϕ
(
x
)
>
ϕ
+
(
x
)
\phi _-(x)>\phi (x)>\phi _+(x)
and also to an infinite interval.