Oscillation Criteria for Third-Order Functional Differential Equations with Damping

This paper is a continuation of the recent study by Bohner et al [9] on oscillation properties of nonlinear third order functional differential equation under the assumption that the second order differential equation is nonoscillatory. We consider both the delayed and advanced case of the studied equation. The presented results correct and extend earlier ones. Several illustrative examples are included.

[1]  C. Swanson,et al.  Comparison and Oscillation Theory of Linear Differential Equations , 2016 .

[2]  Ravi P. Agarwal,et al.  Oscillation Theory for Difference and Functional Differential Equations , 2000 .

[3]  Michal Greguš,et al.  Third Order Linear Differential Equations , 1987 .

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

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

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

[7]  William F. Trench,et al.  Canonical forms and principal systems for general disconjugate equations , 1974 .

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

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

[10]  I. Jadlovská,et al.  Properties of the third order trinomial functional differential equations , 2015 .

[11]  G. Birkhoff One the Solutions of Ordinary Linear Homogeneous Differential Equations of the Third Order , 1911 .

[12]  C. M. Place,et al.  Ordinary Differential Equations , 1982 .

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

[14]  John H Barrett,et al.  Oscillation theory of ordinary linear differential equations , 1969 .