Interval Oscillation Criteria for Second-Order Damped Differential Equations with Mixed Nonlinearities
In this paper, we consider the interval oscillation criteria for second-order damped differential equations with mixed nonlinearities r ( t ) ( x ′ ( t ) ) γ ′ + p ( t ) ( x ′ ( t ) ) γ + ∑ i = 0 n q i ( t ) x ( g i ( t ) ) α i sgn x ( g i ( t ) ) = e ( t ) , where γ is a quotient of odd positive in...
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| Veröffentlicht in: | Bulletin of the Malaysian Mathematical Sciences Society 2016-07, Vol.39 (3), p.861-884 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we consider the interval oscillation criteria for second-order damped differential equations with mixed nonlinearities
r
(
t
)
(
x
′
(
t
)
)
γ
′
+
p
(
t
)
(
x
′
(
t
)
)
γ
+
∑
i
=
0
n
q
i
(
t
)
x
(
g
i
(
t
)
)
α
i
sgn
x
(
g
i
(
t
)
)
=
e
(
t
)
,
where
γ
is a quotient of odd positive integers,
α
0
=
γ
,
α
i
>
0
,
i
=
1
,
2
,
…
,
n
with
r
,
p
,
e
, and
q
i
∈
C
(
[
t
0
,
∞
)
,
R
)
,
r
(
t
)
>
0
,
g
i
:
R
→
R
are nondecreasing continuous functions on
R
and
lim
t
→
∞
g
i
(
t
)
=
∞
,
i
=
0
,
1
,
2
,
…
,
n
.
Our results in this paper extend and improve some known results. Some examples are given here to illustrate our main results. |
|---|---|
| ISSN: | 0126-6705 2180-4206 |
| DOI: | 10.1007/s40840-015-0193-2 |