Oscillation Criteria for Functional Nonlinear Dynamic Equations with γ -Laplacian, Damping and Nonlinearities Given by Riemann–Stieltjes Integrals
In this paper, we present oscillation criteria for the second-order nonlinear dynamic equation [ a ( t ) ϕ γ ( x Δ ( t ) ) ] Δ + p ( t ) ϕ γ ( x Δ σ ( t ) ) + q 0 ( t ) ϕ γ ( x ( g 0 ( t ) ) ) + ∑ i = 1 2 ∫ a i b i q i ( t , s ) ϕ α i ( s ) ( x ( g i ( t , s ) ) ) Δ ζ i ( s ) = 0 on a time scale T w...
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| Veröffentlicht in: | Mediterranean journal of mathematics 2016-06, Vol.13 (3), p.981-1003 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we present oscillation criteria for the second-order nonlinear dynamic equation
[
a
(
t
)
ϕ
γ
(
x
Δ
(
t
)
)
]
Δ
+
p
(
t
)
ϕ
γ
(
x
Δ
σ
(
t
)
)
+
q
0
(
t
)
ϕ
γ
(
x
(
g
0
(
t
)
)
)
+
∑
i
=
1
2
∫
a
i
b
i
q
i
(
t
,
s
)
ϕ
α
i
(
s
)
(
x
(
g
i
(
t
,
s
)
)
)
Δ
ζ
i
(
s
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=
0
on a time scale
T
which is unbounded above. Our results generalize and improve some known results for oscillation of second-order nonlinear dynamic equation. Some examples are given to illustrate the main results. |
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| ISSN: | 1660-5446 1660-5454 |
| DOI: | 10.1007/s00009-015-0553-z |