Author:
Liu Zeqing,Jia Ming,Ume Jeong Sheok,Kang Shin Min
Abstract
Abstract
This paper deals with the solvability of the higher-order nonlinear neutral delay differential equation
d
n
d
t
n
[
x
(
t
)
+
p
(
t
)
x
(
t
−
τ
)
]
+
(
−
1
)
n
+
1
∑
i
=
1
m
q
i
(
t
)
x
(
α
i
(
t
)
)
+
(
−
1
)
n
+
1
f
(
t
,
x
(
β
1
(
t
)
)
,
…
,
x
(
β
l
(
t
)
)
)
=
r
(
t
)
,
t
≥
t
0
, where
τ
>
0
,
n
,
m
,
l
∈
N
,
p
,
r
,
q
i
,
α
i
,
β
j
∈
C
(
[
t
0
,
+
∞
)
,
R
)
, and
f
∈
C
(
[
t
0
,
+
∞
)
×
R
l
,
R
)
satisfying
lim
t
→
+
∞
α
i
(
t
)
=
lim
t
→
+
∞
β
j
(
t
)
=
+
∞
,
i
∈
{
1
,
2
,
…
,
m
}
,
j
∈
{
1
,
2
,
…
,
l
}
. With respect to various ranges of the function p, we investigate the existence of uncountably many bounded nonoscillatory solutions for the equation. The main tools used in this paper are the Krasnoselskii and Schauder fixed point theorems together with some new techniques. Six nontrivial examples are given to illustrate the superiority of the results presented in this paper.
MSC:39A10, 39A20, 39A22.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference16 articles.
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