Abstract
We present the oscillation criteria for the following neutral dynamic equation on time scales:
$$ \bigl(y(t)-C(t)y(t-\zeta )\bigr)^{\Delta }+P(t)y(t-\eta )-Q(t)y(t-\delta )=0, \quad t\in {\mathbb{T}}, $$
(
y
(
t
)
−
C
(
t
)
y
(
t
−
ζ
)
)
Δ
+
P
(
t
)
y
(
t
−
η
)
−
Q
(
t
)
y
(
t
−
δ
)
=
0
,
t
∈
T
,
where $C, P, Q\in C_{\mathit{rd}}([t_{0},\infty ),{\mathbb{R}}^{+})$
C
,
P
,
Q
∈
C
rd
(
[
t
0
,
∞
)
,
R
+
)
, ${\mathbb{R}} ^{+}=[0,\infty )$
R
+
=
[
0
,
∞
)
, $\gamma , \eta , \delta \in {\mathbb{T}}$
γ
,
η
,
δ
∈
T
and $\gamma >0$
γ
>
0
, $\eta >\delta \geq 0$
η
>
δ
≥
0
. New conditions for the existence of nonoscillatory solutions of the given equation are also obtained.
Oscillation criteria for third-order neutral dynamic equations with continuously distributed delay
