Affiliation:
1. Department of Mathematics Sambalpur University Sambalpur-768019 India
Abstract
Abstract
In this paper, sufficient conditions are established for oscillation of a class of nonlinear fourth order mixed neutral differential equations of the form
1
a
(
t
)
(
(
y
(
t
)
+
p
(
t
)
y
(
t
−
τ
)
)
″
)
α
″
=
q
(
t
)
f
(
y
(
t
−
σ
1
)
)
+
r
(
t
)
g
(
y
(
t
+
σ
2
)
)
$$\left(\frac{1}{a(t)}\bigl((y(t)+p(t)y(t-\tau))''\bigr)^\alpha\right)''=q(t)f(y(t-\sigma_1))+r(t) g(y(t+\sigma_2))$$
under the assumption
∫
0
∞
(
a
(
t
)
)
1
α
d
t
<
∞
$$\int \limits_{0}^{\infty}(a(t))^{\frac{1}{\alpha}}\,{\rm d} t \lt \infty$$
for various ranges of p(t), where α is the ratio of odd positive integers.
Reference12 articles.
1. Agarwal, R. P.—Grace, S. R.—Wong, P. J. Y.: Oscillation of fourth order nonlinear difference equations, Int. J. Difference Equ. 2 (2007), 123—137.
2. Graef, J. R.—Spikes, P. W.: On the oscillation of an n-th order nonlinear neutral delay differential equation, J. Comput. Appl. Math. 41 (1992), 35—40.
3. Gyori, I.—Ladas, G.: Oscillation Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford, 1991.
4. Hale, J. K.: Theory of Functional Differential Equations, Springer-Verlag, New York, 1977.
5. Kusano, T.—Naito, M.: Non-linear oscillation of fourth order differential equations, Canad. J. Math. 4 (1976), 840-852.
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