Affiliation:
1. Department of Mathematics and Computer Science Normal College of Jishou University Jishou Hunan, 416000 P. R. CHINA
2. School of Mathematical Sciences South China Normal University Guangzhou, 510631 P. R. CHINA
Abstract
Abstract
In this paper, we consider the oscillation for the second-order quasi-linear neutral dynamic equation
(
r
(
t
)
|
Z
Δ
(
t
)
|
α
−
1
Z
Δ
(
t
)
)
Δ
+
q
(
t
)
|
x
(
δ
(
t
)
)
|
β
−
1
x
(
δ
(
t
)
)
=
0.
$${(r(t)|{Z^\Delta }(t{)|^{\alpha - 1}}{Z^\Delta }(t))^\Delta } + q(t)|x(\delta (t{))|^{\beta - 1}}x(\delta (t)) = 0.$$
on time scale 𝕋, where Z(t) = x(t) + p(t)x(τ(t)), α,β > 0 are constants. We establish some new oscillation criteria and give sufficient conditions to insure that all solutions of quasi-linear neutral dynamic equation are oscillatory on time scale 𝕋. The new oscillation criteria are presented that improve some known results in the literature.
Cited by
1 articles.
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