Oscillation of third-order nonlinear damped delay differential equations

This paper is concerned with the oscillation of certain third-order nonlinear delay differential equations with damping. We give new characterizations of oscillation of the third-order equation in terms of oscillation of a related, well-studied, second-order linear differential equation without damping. We also establish new oscillation results for the third-order equation by using the integral averaging technique due to Philos. Numerous examples are given throughout.

[1]  Said R. Grace,et al.  On oscillation and nonoscillation of general functional differential equations , 1985 .

[2]  Ravi P. Agarwal,et al.  A Philos-type theorem for third-order nonlinear retarded dynamic equations , 2014, Appl. Math. Comput..

[3]  Aydin Tiryaki,et al.  Asymptotic behaviour of a class of nonlinear functional differential equations of third order , 2001, Appl. Math. Lett..

[4]  Samir H. Saker,et al.  OSCILLATION CRITERIA OF THIRD-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS , 2006 .

[5]  Ravi P. Agarwal,et al.  Hille and Nehari type criteria for third-order delay dynamic equations , 2013 .

[6]  John R. Graef,et al.  On the oscillation of third order neutral delay dynamic equations on time scales , 2012, Comput. Math. Appl..

[7]  Ravi P. Agarwal,et al.  On oscillation criteria for third order nonlinear delay differential equations , 2009 .

[8]  N. Parhi,et al.  On asymptotic behavior of delay-differential equations of third order 1 1 This work is supported by , 1998 .

[9]  Anton Škerlík,et al.  Integral criteria of oscillation for a third order linear differential equation , 1995 .

[10]  Mustafa Aktaş,et al.  Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping , 2007 .

[11]  Seshadev Padhi,et al.  Theory of Third-Order Differential Equations , 2013 .

[12]  Mauro Marini,et al.  On the oscillatory behavior of a third order nonlinear differential equation , 1990 .

[13]  George Seifert,et al.  Oscillation Theory of Delay Differential Equations (I. Györi and G. Ladas); Oscillation Theory for Neutral Differential Equations with Delay (D. D. Bainov and D. P. Mishev) , 1993, SIAM Rev..

[14]  Ioannis P. Stavroulakis,et al.  Necessary and Sufficient Conditions for Oscillations of Higher Order Delay Differential Equations , 1984 .

[15]  Mauro Marini,et al.  Oscillation Results for Emden–Fowler Type Differential Equations , 1997 .

[16]  N. Parhi,et al.  Asymptotic property of solutions of a class of third-order differential equations , 1990 .

[17]  G. Ladas,et al.  Oscillation Theory of Delay Differential Equations: With Applications , 1992 .

[18]  Ravi P. Agarwal,et al.  Oscillation Theory for Second Order Dynamic Equations , 2002 .

[19]  Agacik Zafer,et al.  Oscillation criteria for third-order nonlinear functional differential equations , 2010, Appl. Math. Lett..

[20]  C. Philos,et al.  Oscillation theorems for linear differential equations of second order , 1989 .

[21]  Ravi P. Agarwal,et al.  Oscillation and asymptotic behavior of third-order nonlinear retarded dynamic equations , 2012, Appl. Math. Comput..

[22]  N. Parhi,et al.  Oscillation criteria for a class of nonlinear differential equations of third order , 1992 .

[23]  Ravi P. Agarwal,et al.  OSCILLATION OF THIRD-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS , 2013 .