On Oscillation of Solutions of Linear Differential Equations
An interrelationship is found between the accumulation points of zeros of non-trivial solutions of f ′ ′ + A f = 0 and the boundary behavior of the analytic coefficient A in the unit disc D of the complex plane C . It is also shown that the geometric distribution of zeros of any non-trivial solution...
Gespeichert in:
| Veröffentlicht in: | The Journal of Geometric Analysis 2017, Vol.27 (1), p.868-885 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | An interrelationship is found between the accumulation points of zeros of non-trivial solutions of
f
′
′
+
A
f
=
0
and the boundary behavior of the analytic coefficient
A
in the unit disc
D
of the complex plane
C
. It is also shown that the geometric distribution of zeros of any non-trivial solution of
f
′
′
+
A
f
=
0
is severely restricted if
*
|
A
(
z
)
|
1
-
|
z
|
2
2
≤
1
+
C
1
-
|
z
|
,
z
∈
D
,
for any constant
0
<
C
<
∞
. These considerations are related to the open problem of whether (
*
) implies finite oscillation for all non-trivial solutions. |
|---|---|
| ISSN: | 1050-6926 1559-002X |
| DOI: | 10.1007/s12220-016-9701-3 |