Oscillation Conditions for a Class of Lienard Equation

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.