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Properties of the third order trinomial differential equations with delay argument. (English) Zbl 1173.34348
Summary: We study properties of the third order trinomial delay differential equation $$y^{\prime \prime \prime }(t)+p(t)y{^{\prime}}(t)+g(t)y(\tau (t))=0$$ by transforming this equation to a binomial second/third order differential equation. Employing suitable comparison theorems we establish new results on the asymptotic behavior of solutions.

MSC:
34K25Asymptotic theory of functional-differential equations
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References:
[1] Erbe, L.: Existence of oscillatory solutions and asymptotic behavior for a class of third order linear differential equation. Pacific J. Math. 64, 369-385 (1976) · Zbl 0339.34030
[2] Greguš, M.: Asymptotic properties of solutions of nonautonomous ordinary differential equations. (1981)
[3] Jones, G. D.: An asymptotic property of solutions y”’+$p(x)$y’+$q(x)$y=0. Pacific J. Math. 47, 135-138 (1973) · Zbl 0264.34040
[4] Lazer, A. C.: The behavior of solutions of the differential equation y”’+$p(x)$y’+$q(x)$y=0. Pacific J. Math. 17, 435-466 (1966) · Zbl 0143.31501
[5] Škerlík, A.: Integral criteria of oscillation for the third order linear differential equations. Math. slovaca 45, 403-412 (1995) · Zbl 0855.34038
[6] Chanturija, T. A.; Kiguradze, I. T.: Asymptotic properties of nonautonomous ordinary differential equations. (1990)
[7] Džurina, J.: Comparison theorems for functional differential equations. (2002)
[8] Džurina, J.: Comparison theorems for nonlinear ODE’s. Math. slovaca 42, 299-315 (1992) · Zbl 0760.34030
[9] Kusano, T.; Naito, M.: Comparison theorems for functional differential equations with deviating arguments. J. math. Soc. Japan 3, 509-532 (1981) · Zbl 0494.34049
[10] Kusano, T.; Naito, M.; Tanaka, K.: Oscillatory and asymptotic behavior of solutions of a class of linear ordinary differential equations. Proc. roy. Soc. edinburg 90, 25-40 (1981) · Zbl 0486.34021
[11] Tanaka, K.: Asymptotic analysis of odd order ordinary differential equations. Hiroshima math. J. 10, 391-408 (1980) · Zbl 0453.34033
[12] Bartušek, M.; Cecchi, M.; Došlá, Z.; Marini, M.: On nonoscillatory solutions of third order nonlinear differential equations. Dynam. systems appl. 9, 483-500 (2000)
[13] Cecchi, M.; Došlá, Z.; Marini, M.: On the third order differential equations with property A and B. J. math. Anal. appl. 231, 509-525 (1999) · Zbl 0926.34025
[14] Džurina, J.: Asymptotic properties of the third order delay differential equations. Nonlinear anal. 26, 33-39 (1996) · Zbl 0840.34076
[15] Parhi, N.; Padhi, S.: On asymptotic behaviour of delay differential equations of third order. Nonlinear anal. 34, 391-403 (1998) · Zbl 0935.34063
[16] Bellman, R.: Stability theory of differential equations. 13 (1953) · Zbl 0053.24705