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and the only possible passages between
Ω
−
and
Ω
+
are
+
+
+
−
←
+
−
+
−
→
+
−
−
−
,
−
−
+
+
←
+
−
+
+
→
+
+
+
+
,
−
−
−
+
←
+
−
−
+
→
+
−
−
−
,
+
+
+
+
←
+
+
−
+
→
+
+
−
−
,
−
−
−
+
←
−
+
−
+
→
−
+
+
+
,
+
+
−
−
←
−
+
−
−
→
−
−
−
−
,
+
+
+
−
←
−
+
+
−
→
−
+
+
+
,
−
−
−
−
←
−
−
+
−
→
−
−
+
+
,
always from
Ω
−
to
Ω
+
.
So, any trajectory generated by a non-trivial solution can perform only
one passage between
Ω
−
and
Ω
+
,
which can be only from
Ω
−
to
Ω
+
.
I
Lemma 4.
There exist trajectories of all three types mentioned in
Lemma 3, namely
•
trajectories lying completely in
Ω
−
;
•
trajectories lying completely in
Ω
+
;
•
trajectories with a single passage
Ω
−
→
Ω
+
.
J
Any solution to (1) with initial data corresponding to a point from
Ω
−
∩
Ω
+
generates a trajectory of the 3rd type. E.g., the solution with initial
data
y
0
(0) = 0
, y
(0) =
y
00
(0) =
y
000
(0) = 1
generates a trajectory with the
passage
+
−
+
+
⊂
Ω
−
→
+
+
+
+
⊂
Ω
+
.
If there exists a solution
y
(
x
)
to (1) generating a trajectory lying
completely in
Ω
−
,
then the function
z
(
x
) =
y
(
−
x
)
is also a solution
10
ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. “Естественные науки”. 2015. № 2