In this paper the oscillatory behavior of solutions of a class of a generalized Lienard equation is studded. We give some new criteria for the oscillation of a class of generalized Lienard equation. Several oscillation criteria are presented that improve the results obtained in the literature by using the refined integral averaging technique are extended. Moreover, three examples are given to illustrate the theoretical analysis.

1.
H. Kh.
Abdullah
,
On the Oscillation of Second Order Nonlinear Differential Equations
.
International Journal of Applied Mathematical Research
.
3
, No.
1
, pp
1
6
. (
2013
),
2.
H. Kh.
Abdullah
,
Oscillation Criteria of Second Order Nonlinear Differential Equations
.
Open Journal of Applied Science
2
No.
4
pp
120
122
(
2013
).
3.
H. Kh.
Abdullah
,
The Oscillation of the Nonlinear Differential Equations x¨(t)+g(x(t))(x˙(t))2+f(t)x˙(t)+r(t)h(x(t))=0
,
International Journal of Pure and Applied Mathematics
,
94
No.
1
pp
1
7
. (
2014
).
4.
H. Kh.
Abdullah
,
Sufficient Conditions for Oscillation of Second Order Nonlinear Differential Equations
International Journal of Differential Equations and Applications
,
12
No.
3
pp
192
197
(
2013
).
5.
H. Kh.
Abdullah
,
Oscillation Conditions of Second Order Nonlinear Differential Equations
.
International Journal of Applied Mathematical science
,
34
, No.
1
pp
1490
1497
. (
2014
).
6.
RP
Agarwal
,
C
Avramescu
,
OG
,
Mustafa
,
On the oscillation theory of a second order strictly sublinear differential equation
.
Can. Math. Bull.
53
, pp
193
203
. (
2010
).
7.
S
Breuer
. and
D
Gottlieb
.:
Hille-Wintner type oscillation criteria for linear ordinary differential equations of second order
,
Ann. Polon. Math.
30
, pp
257
262
(
1975
).
8.
D
Cakmak
.:
Oscillation for second order nonlinear differential equations with damping
,
Dynam. Systems Appl.
,
17
, No.
1
pp
139
148
(
2008
).
9.
Fu
,
XL
,
Li
,
TX
,
CH
Zhang
,
Oscillation of second-order damped differential equations
.
Adv. Differ. Equ.
2013
,
326
(
2013
).
10.
W. J
Close
.
Oscillation criteria for nonlinear second order equations
,
Ann. Mat. Pura Appl.
,
82
pp
123
134
(
1969
).
11.
J. Li
Horng
,
Nonoscillatory characterization of a second order linear differential equations
,
Math. Nacher
,
219
, pp
147
161
(
2000
).
12.
R. J.
Kim
,
Oscillation criteria of differential equations of second order
,
Korean J. Math.
,
19
, No.
3
, pp
309
319
(
2011
).
13.
Li
W.
and
R. P
Agarwal
.,
Interval oscillation criteria for second order nonlinear differential equations with damping
,
Compute. Math. Appl.
,
40
, pp
217
230
. (
2000
).
14.
J.
Prausnitz
,
R
Lichtenthaler
,. and
E.
de Azevedo
,
Molecular thermodynamics for fluid-place equilibrium
,
Prentice-Hall, Inc
. (
1986
).
15.
W.T.
Reid
,
Sturmian Theory for Ordinary Differential Equations
,
Springer - Verlay
,
New york
(
1980
).
16.
Sabatini
M.
:
On the period function of x˝ + f(x)(x’)2 + g(x) = 0
,
J. Differential Equations
,
196
pp
151
168
(
2004
).
17.
J.
Tyagi
,
An oscillation theorem for a second order nonlinear differential equations with variable potential
,
Electronic Journal of Differential Equations
,
2009
, No.
19
1
5
(
2009
).
18.
J. S. W
Wong
.,
oscillation criteria for second order nonlinear differential equations with integrable coefficients
,
Proc. Amer. Math.Soc.
,
115
, pp
389
395
(
1992
).
19.
QX
Zhang
and
L
Wang
,
Oscillatory behavior of solutions for a class of second order nonlinear differential equation with perturbation
.
Acta Appl. Math.
110
, pp
885
893
(
2010
).
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