Properties of the third order trinomial differential equations with delay argument

Abstract In this paper we study properties of the third order trinomial delay differential equation y ‴ ( t ) + p ( t ) y ′ ( t ) + g ( t ) y ( τ ( t ) ) = 0 by transforming this equation to binomial second/third order differential equation. Employing suitable comparison theorems we establish new results on asymptotic behavior of solutions of the studied equation.

[1]  Jozef Džurina,et al.  Comparison Theorems for Functional Differential Equations , 1993 .

[2]  Ivan Mojsej,et al.  On bounded nonoscillatory solutions of third-order nonlinear differential equations , 2009 .

[3]  Jozef Džurina Asymptotic properties of the third order delay differential equations , 1996 .

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

[5]  R. Bellman Stability theory of differential equations , 1953 .

[6]  T. Kusano,et al.  Oscillatory and asymptotic behaviour of solutions of a class of linear ordinary differential equations , 1981, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

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

[8]  Gary Douglas Jones An asymptotic property of solutions of y′′′ + py′ + qy = 0 , 1973 .

[9]  Mauro Marini,et al.  On Third Order Differential Equations with Property A and B , 1999 .

[10]  Kyoko Tanaka Asymptotic analysis of odd order ordinary differential equations , 1980 .

[11]  A. Lazer,et al.  The behavior of solutions of the differential equation y′′′ + p(x)y′ + q(x)y = 0 , 1966 .

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

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

[14]  L. Erbe,et al.  EXISTENCE OF OSCILLATORY SOLUTIONS AND ASYMPTOTIC BEHAVIOR FOR A CLASS OF THIRD ORDER LINEAR DIFFERENTIAL EQUATIONS , 1976 .