Oscillation criteria for a class of third order damped differential equations

Abstract The present study concerns the oscillation of a class of third-order nonlinear delay differential equations with middle term. We offer a new description of oscillation of the third-order equations in terms of oscillation of a related well studied second-order linear differential equation without damping. By using the integral averaging technique, we establish new oscillation results for this equation. Some examples are provided to illustrate the main results.

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

[2]  G. D. Jones.  Oscillation Criteria for Third Order Differential Equations , 1976 .

[3]  B. Baculíková,et al.  Oscillation of third-order neutral differential equations , 2010, Math. Comput. Model..

[4]  J. Džurina,et al.  Oscillation of second order neutral delay differential equations , 2009 .

[5]  Maurice Hanan,et al.  Oscillation criteria for third-order linear differential equations. , 1961 .

[6]  E. Elabbasy,et al.  On the Oscillation of Third Order Neutral Differential Equations , 2015 .

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

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

[9]  Blanka Baculíková,et al.  Oscillation of third order trinomial delay differential equations , 2012, Appl. Math. Comput..

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

[11]  E. Elabbasy,et al.  Oscillation Properties of Third Order Neutral Delay Differential Equations , 2016 .

[12]  Martin Bohner,et al.  Oscillation of third-order nonlinear damped delay differential equations , 2016, Appl. Math. Comput..

[13]  Osama Moaaz,et al.  OSCILLATION BEHAVIOR OF SECOND ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS , 2012 .

[14]  E. Elabbasy,et al.  Boundedness and Oscillation of Third Order Neutral Differential Equations with Deviating Arguments , 2015 .

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

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

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

[18]  Ravi P. Agarwal,et al.  On the oscillation of certain functional differential equations via comparison methods , 2003 .

[19]  S. Grace.  Oscillation criteria for third order nonlinear delay differential equations with damping , 2015 .

[20]  B. Baculíková,et al.  Oscillation criteria for third-order nonlinear differential equations , 2008 .