On the oscillation of third order quasilinear  delay differential equations with Maxima

R. Arula,* and M. Manib

On the oscillation of third order quasilinear delay differential equations with Maxima

Authors :

R. Arul^a,* and M. Mani^b

Author Address :

a,bDepartment of Mathematics, Kandaswami Kandar’s College, Velur–638 182, Tamil Nadu, India.

Abstract :

In this paper, we study the oscillation and asymptotic properties of third order quasilinear neutral delay differential equation
e
left( a(t) left( (x(t)+p(t)x( au(t)))’’ ight)^alpha ight)’+q(t)max_{[sigma(t), t]}x^alpha(s)=0,~~tgeq t_0 geq 0
ee
where $alpha$ is a ratio of odd positive integers and $int_{t_0}^infty frac{1}{a^{1/ alpha}(t)}dt=infty$. We establish a new condition which guarantees that every solution of (0.1) is either oscillatory or converges to zero. There results extend some known results in the literature without ``maxima’’. Examples are given to illustrate the main results.

Keywords :

Oscillation, quasilinear, neutral, delay, third order, differential equations with maxima.

DOI :

Article Info :

Received : March 27, 2014; Accepted : August 02, 2014.