INTERVAL OSCILLATION CRITERIA FOR SECOND-ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

This paper concerns the oscillation problem of a general class of second-order differential equations. New interval oscillation criteria for a class of second- order functional nonlinear differential equations with damping and forcing terms have been established by using the classical Riccati technique and averaging function of Philos type. Obtained results extend some of previous works and particularly answer a comment published previously. Illustrative examples also stated.

Keywords:

Differential equation, functional term oscillati.,

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[1] J.S.W. Wong, On Kamenev-type oscillation for second order differential equations with damping, J. Math. Anal. Appl. 248 (2001) 244–257.
[2] X. Yang, Oscillation criteria for nonlinear differential equations with damping, Applied Mathematics and Computation 136 (2003) 549–557.
[3] Y.V. Rogovchenko, Oscillation theorems for second order equations with damping, Nonlinear Anal. 41 (2000) 1005–1028.
[4] A. Tiryaki and A. Zafer, Oscillation criteria for second order nonlinear differential equation with damping, Turkish J. Math. 24 (2000) 185–196.
[5] O.G. Mustafa and S.P. Rogovchenko, Oscillation of nonlinear second order differential equations with damping term, J. Math. Anal. Appl. 298 (2004) 604–620.
[6] S.P. Rogovchenko and Yu.V. Rogovchenko, Oscillation of second order differential equations with damping, Dynam. Contin. Discrete Impuls. Syst. Ser. A 10 (2003) 447–461.
[7] B. Ayanlar and A. Tiryaki, Oscillation theorems for nonlinear second order differential equation with damping, Acta Math. Hungar. 89 (2000) 1-13.
[8] S.P. Rogovchenko and Yu.V. Rogovchenko, Oscillation theorems for differential equations with a nonlinear damping term, J. Math. Anal. Appl.279 (2003) 139–152.
[9] A. Tiryaki and A. Zafer, Interval oscillation of a general class of second-order nonlinear differential equations with nonlinear damping, Nonlinear Anal. 60 (2005) 49–63.
[10] M. Bayram, A. Seçer, H. Adıgüzel, Oscillatory behavior of solutions of differential equations with fractional order, Appliead Mathematics & Information Sciences, 11 (3) 683-691.
[11] M. Bayram, A. Seçer, H. Adıgüzel, On the oscillation of fractional order nonlinear differential equations, Sakarya University Journal of Science, 21 (6) 1-20.
[12] M. Bayram, H. Adıgüzel, A. Seçer, Oscillation criteria for nonlinear fractional differential equation with damping term, Open Physics, 14 (1) 119-128.
[13] X. Zhao and F. Meng , Oscillation of second-order nonlinear ODE with damping, Applied Mathematics and Computation 182 (2006) 1861–1871.
[14] D. Çakmak and A. Tiryaki, Comment on the paper “Oscillation of second-ordernonlinear ODE with damping”, Applied Mathematics and Computation 191 (2007) 298.
[15] Y. Huang and F. Meng, Oscillation of second-order nonlinear ODE with damping, Applied Mathematics and Computation 199 (2008) 644–652.
[16] N.Shang and H. Qin, Comments on the paper: “Oscillation of second-order nonlinear ODEwith damping” [Applied Mathematics and Computation 199 (2008) 644–652], Applied Mathematics and Computation 218 (2011) 2979–2980.
[17] F. Meng and Y. Huang, Interval oscillation criteria for a forced second-order nonlinear differential equations with damping, Applied Mathematics and Computation 218 (2011) 1857-1861.
[18] Y. Huang and F. Meng, Oscillation criteria for forced second-order nonlinear differential equations with damping, Journal of Computational and Applied Mathematics 224 (2009) 339-345.
[19] G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities, second ed., Cambridge University Press, Cambridge, 1988.
[20] A. Tiryaki and Y Başçı, Interval oscillation criteria for second-order quasi-linear functional differential equations, Dynamics of Continuous, Discrete and Impulsive Systems Serias A: Mathematical Analysis 16 (2009) 233-252.

Sigma Mühendislik ve Fen Bilimleri Dergisi-Cover

ISSN: 1304-7191
Yayın Aralığı: Yılda 4 Sayı
Yayıncı: Yıldız Teknik Üniversitesi

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