oalogo2  

AUTHOR(S): 

Hishyar Kh. Abdullah

 

TITLE

Oscillation Conditions for a Class of Lienard Equation

pdf PDF

ABSTRACT

The aim of this paper is to investigate oscillatory properties of a class of a generalized Lienard equation .Several oscillation conditions are presented that improve the results obtained in the literature. The results obtained here are new and further improve and complement some known results in the literature. We extend and improve the oscillation criteria of several authors. Moreover, two examples are presented to demonstrate the main results.

KEYWORDS

Oscillatory, Lienard equation, Second order differential equations, Non-Linear

REFERENCES

[1] H. Kh. Abdullah, On the Oscillation of Second Order Nonlinear Differential Equations, International Journal of Applied Mathematical Research, Vol.3, No.1, 2013, pp. 1-6. 

[2] H. Kh. Abdullah, Oscillation Criteria of Second Order Nonlinear Differential Equations, Open Journal of Applied Science, Vol.2, No.4, 2013, pp. 120-122. 

[3] H. Kh. Abdullah, The Oscillation of the Nonlinear Differential Equations ??̈(??) + ?(?) + ?(?(?) + ?(?)?(?) + ?(?)ℎ(?(?)) =0, International Journal of Pure and Applied Mathematics, Vol.94 No.1, 2014, pp. 1-7. 

[4] H. Kh. Abdullah, Sufficient Conditions for Oscillation of Second Order Nonlinear Differential Equations, International Journal of Differential Equations and Applications, Vol.12 No.3, 2013, pp. 192- 197. 

[5] H. Kh. Abdullah, Oscillation Conditions of Second Order Nonlinear Differential Equations, International Journal of Applied Mathematical science, Vol.34 No.1, 2014, pp. 1490-1497. 

[6] S.Breuer and D. Gottlieb, Hille-Wintner type oscillation criteria for linear ordinary differential equations of second order, Ann. Polon. Math, Vol.30, 1975, pp. 257-262. 

[7] D.Cakmak, Oscillation for second order nonlinear differential equations with damping, Dynam. Systems Appl., Vol.17 No.1, 2008, pp. 139-148. 

[8] W. J. Close, Oscillation criteria for nonlinear second order equations, Ann. Mat. Pura Appl., Vol.82, 1969, pp. 123-134. 

[9] J. Li Horng, Nonoscillatory characterization of a second order linear differential equations, Math. Nacher, Vol.219, 2000, pp. 147-161. 

[10] R. J Kim, Oscillation criteria of differential equations of second order, Korean J. Math., Vol.19 No.3, 2011, pp. 309-319. 

[11] W. Li and R. P. Agarwal, Interval oscillation criteria for second order nonlinear differential equations with damping, compute. Math. Appl., Vol.40, 2000, pp. 217-230. 

[12] W. T. Reid, Sturmian Theory for Ordinary Differential, Springer - Verlay, New York, 1980. 

[13] M. Sabatini, On the period function of?′′ + ?(?)(?′ )2 + ?(?) = 0, J. Differential Equations, Vol.196, 2004, pp. 151-168. 

[14] J. Tyagi, An oscillation theorem for a second order nonlinear differential equations with variable potential, Electronic Journal of Differential Equations, Vol.2009 No.19, 2009, pp. 1-5. 

[15] J. S. W. Wong, oscillation criteria for second order nonlinear differential equations with integrable coefficients, Proc. Amer. Math.Soc., Vol.115, 1992, pp. 389- 395.

Cite this paper

Hishyar Kh. Abdullah. (2016) Oscillation Conditions for a Class of Lienard Equation. Mathematical and Computational Methods, 1, 325-329

 

cc.png
Copyright © 2016 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0