Abstract
AbstractWe study the oscillatory property of the higher-order trinomial differential equation with advanced effects $$ x^{(n)}(t)+p(t)x'(t)+q(t)x \bigl(\sigma (t) \bigr)=0,\quad \sigma (t) \geq t. $$
x
(
n
)
(
t
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+
p
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t
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x
′
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t
)
+
q
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t
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x
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σ
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t
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)
=
0
,
σ
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t
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≥
t
.
Suppose that all solutions of the corresponding ($n-1$
n
−
1
)th-order two-term differential equation $$ y^{(n-1)}(t)+p(t)y(t)=0 $$
y
(
n
−
1
)
(
t
)
+
p
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t
)
y
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t
)
=
0
are non-oscillatory. In order to supplement the research in the theory of oscillation proposed by (Džurina et al. in Electron. J. Differ. Equ. 2015:70, 2015), two types of clearly confirmable criteria for oscillatory behavior of the investigated equation are obtained. Some examples are offered to describe our main results.
Funder
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
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