Oscillation of second order neutral dynamic equations with deviating arguments on time scales
In this paper, we consider the following second order neutral dynamic equations with deviating arguments on time scales: ( r ( t ) ( z Δ ( t ) ) α ) Δ + q ( t ) f ( y ( m ( t ) ) ) = 0 , where z ( t ) = y ( t ) + p ( t ) y ( τ ( t ) ) , m ( t ) ≤ t or m ( t ) ≥ t , and τ ( t ) ≤ t . Some new oscilla...
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| Veröffentlicht in: | Advances in difference equations 2018-09, Vol.2018 (1), p.1-10, Article 337 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we consider the following second order neutral dynamic equations with deviating arguments on time scales:
(
r
(
t
)
(
z
Δ
(
t
)
)
α
)
Δ
+
q
(
t
)
f
(
y
(
m
(
t
)
)
)
=
0
,
where
z
(
t
)
=
y
(
t
)
+
p
(
t
)
y
(
τ
(
t
)
)
,
m
(
t
)
≤
t
or
m
(
t
)
≥
t
, and
τ
(
t
)
≤
t
. Some new oscillatory criteria are obtained by means of the inequality technique and a Riccati transformation. Our results extend and improve many well-known results for oscillation of second order dynamic equations. Some examples are given to illustrate the main results. |
|---|---|
| ISSN: | 1687-1847 1687-1839 1687-1847 |
| DOI: | 10.1186/s13662-018-1773-x |