Asymptotics and oscillation of nth-order nonlinear differential equations with p-Laplacian like operators
This paper is concerned with n th-order nonlinear differential equations of the form ( a ( t ) | x ( n − 1 ) ( t ) | p − 2 x ( n − 1 ) ( t ) ) ′ + r ( t ) | x ( n − 1 ) ( t ) | p − 2 x ( n − 1 ) ( t ) + q ( t ) | x ( g ( t ) ) | p − 2 x ( g ( t ) ) = 0 with n ≥ 2 . By discussing the signs of i th-or...
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| Veröffentlicht in: | Advances in difference equations 2015-11, Vol.2015 (1), p.1-16, Article 357 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | This paper is concerned with
n
th-order nonlinear differential equations of the form
(
a
(
t
)
|
x
(
n
−
1
)
(
t
)
|
p
−
2
x
(
n
−
1
)
(
t
)
)
′
+
r
(
t
)
|
x
(
n
−
1
)
(
t
)
|
p
−
2
x
(
n
−
1
)
(
t
)
+
q
(
t
)
|
x
(
g
(
t
)
)
|
p
−
2
x
(
g
(
t
)
)
=
0
with
n
≥
2
. By discussing the signs of
i
th-order derivatives of eventually positive solutions, for
i
=
1
,
…
,
n
−
1
, and using the generalized Riccati technique and integral averaging technique, we derive new criteria for oscillation and asymptotic behavior of the equation. Our results generalize and improve many existing results in the literature. |
|---|---|
| ISSN: | 1687-1847 1687-1839 1687-1847 |
| DOI: | 10.1186/s13662-015-0689-y |