Oscillation Theorems for Third Order Nonlinear Delay Differential Equation with “Maxima”

R. Arul; A. Ashok

R. Arul Department of Mathematics, Kandaswami Kandar’s College Velur - 638 182, Namakkal Dt. Tamil Nadu, India
A. Ashok Department of Mathematics, Kandaswami Kandar’s College Velur - 638 182, Namakkal Dt. Tamil Nadu, India

Keywords: Oscillation, third order, differential equation with maxima.

Abstract

In this paper we obtain oscillation criteria for the third order delay differential equation with “maxima” of the form

via comparison with the oscillatory behavior of first order differential equations. Some examples are given to illustrate the main results

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References

R.Arul and M.Mani, On the oscillation of third order quasilinear delay differential equations with “maxima”, Malaya J. Mathematik, 2 (2014), 489-496.

R.Arul and M.Mani, Oscillation of third order nonlinear delay differential equation with “maxima”, Communications in Differential and Difference Equations, 5 (2014), 25-34.

R.Arul and M.Mani, Oscillation solution to third order half-linear neutal differential equation with “maxima”, Far East J. Math. Sci., 90 (2014), 89-101.

D.Bainov and S.G.Hristova, Differential Equations with “Maxima”, CRC Press, New York, 2011.

D.Bainov, V.Petrov and V.Proytcheva, Oscillation of neutral differential equations with ’maxima’, Rev. Math. Univ. Comput. Madrid., 8 (1995), 171-180.

L.H.Erbe, Q.Kong and B.G.Zhang, Oscillation Theory For Functional Differential Equations, Marcel Dekker, New York, 1995.

G.S.Ladde, V.Lakshmikantham and B.G.Zhang, Oscillation Theory for Differential Equations with Deviating Arguments, Dekker, New York, 1987.

Ch.G.Philos, On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delay, Arch. Math., 36, (1981), 168-178.

E.P.Popov, Automatic Regulation and Control, Nauka, Moscow, 1996.