Affiliation:
1. Department of Mathematics and Computer Science , Faculty of Science Menoufia University , Menoufia , Egypt
Abstract
Abstract
A class of third order differential equations with several sublinear neutral terms of the type
(
a
(
t
)
(
b
(
t
)
(
x
(
t
)
+
∑
j
=
1
n
p
j
(
t
)
x
α
j
(
τ
j
(
t
)
)
)
′
)
′
)
′
+
∑
i
=
1
m
f
i
(
t
,
x
(
σ
i
(
t
)
)
)
=
0
,
t
≥
t
0
>
0
$$\begin{array}{}
\displaystyle
\bigg( a(t)\Big( b(t)\Big(x(t)+\sum\limits_{j=1}^{n}p_{j}(t)x^{\alpha _{j}}(\tau
_{j}(t))\Big)'\Big)'\bigg)'
+\sum\limits_{i=1}^{m}f_{i}(t,x(\sigma _{i}(t)))=0,\qquad t\geq
t_{0} \gt 0
\end{array}$$
is considered. Some oscillation criteria are presented to improve and complement those in the literature. Two examples are established to illustrate the main results.
Reference18 articles.
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2. Chatzarakis, G. E.—Grace, S. R.—Jadlovská, I.: Oscillation criteria for third-order delay differential equations, Adv. Difference Equ. 330 (2017), 11 pages.
3. Cloud, M. J.—Drachman, B. C.: Inequalities with Applications to Engineering, Springer-Verlag, NewYork, Inc. 1998.
4. Došlá, Z.—Liška, P.: Oscillation of third-order nonlinear neutral differential equations, Appl. Math. Lett. 56 (2016), 42–48.
5. Došlá, Z.—Liška, P.: Comparison theorems for third-order neutral differential equations, Electron. J. Differential Equations 2016 (2016), 1–13.
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