Affiliation:
1. Department of Mathematics Mendel University in Brno Zemědělská 1 CZ-613 00 Brno Czech Republic
Abstract
Abstract
In this paper we derive oscillation criteria for the second order half-linear neutral differential equation
[
r
(
t
)
Φ
(
z
′
(
t
)
)
]
′
+
c
(
t
)
Φ
(
x
(
σ
(
t
)
)
)
=
0
,
z
(
t
)
=
x
(
t
)
+
b
(
t
)
x
(
τ
(
t
)
)
,
$$ \displaystyle \Bigl[r(t)\Phi(z'(t))\Bigr]'+c(t)\Phi(x(\sigma(t)))=0, \quad z(t)=x(t)+b(t)x(\tau(t)), $$
where Φ(t) = |t|
p−2
t, p ≥ 2, is a power type nonlinearity. We improve recent results published in the literature by obtaining better oscillation constants and removing the usual condition σ(τ(t)) = τ(σ(t)). Two methods (comparison method and Riccati equation method) are used.
Cited by
12 articles.
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