On Sharp Oscillation Criteria for General Third-Order Delay Differential Equations

In this paper, effective oscillation criteria for third-order delay differential equations of the form, r2r1y′′′(t)+q(t)y(τ(t))=0 ensuring that any nonoscillatory solution tends to zero asymptotically, are established. The results become sharp when applied to a Euler-type delay differential equation and, to the best of our knowledge, improve all existing results from the literature. Examples are provided to illustrate the importance of the main results.

[1]  I. T. Kiguradze,et al.  Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations , 1992 .

[2]  M. Bohner,et al.  Oscillation Criteria for Third-Order Functional Differential Equations with Damping , 2016 .

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

[4]  Ravi P. Agarwal,et al.  On the oscillation of certain third order nonlinear functional differential equations , 2008, Appl. Math. Comput..

[5]  I. Jadlovská,et al.  A sharp oscillation result for second-order half-linear noncanonical delay differential equations , 2020 .

[6]  Irena Jadlovská,et al.  Oscillation criteria of Kneser-type for second-order half-linear advanced differential equations , 2020, Appl. Math. Lett..

[7]  G. Chatzarakis,et al.  Oscillation criteria for third-order delay differential equations , 2017 .

[8]  E. Elabbasy,et al.  Oscillation Criteria for Third Order Delay Nonlinear Differential Equations , 2022 .

[9]  T. Candan,et al.  Oscillation of third order functional differential equations with delay. , 2003 .

[10]  N. Mukherjee,et al.  The influence of minimalp-subgroups on the structure of finite groups , 1985 .

[11]  M. Marini,et al.  Disconjugate operators and related differential equations. , 1999 .

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

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

[14]  M. Marini,et al.  Some properties of third order differential operators , 1997 .

[15]  Jozef Dzurina,et al.  Kneser-type oscillation criteria for second-order half-linear delay differential equations , 2020, Appl. Math. Comput..

[16]  B. Baculíková,et al.  Oscillation of third-order functional differential equations , 2010 .

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

[18]  S. Saker,et al.  On the oscillation of certain class of third-order nonlinear delay differential equations , 2010 .

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

[20]  J. Graef,et al.  SHARP ASYMPTOTIC RESULTS FOR THIRD-ORDER LINEAR DELAY DIFFERENTIAL EQUATIONS , 2020 .

[21]  Manabu Naito,et al.  Comparison theorems for functional differential equations with deviating arguments , 1981 .