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

R. Arul; M. Mani

doi:10.26637/mjm204/016

Abstract

In this paper, we study the oscillation and asymptotic properties of third order quasilinear neutral delay differential equation
$$
\left(a(t)\left((x(t)+p(t) x(\tau(t)))^{\prime \prime}\right)^\alpha\right)^{\prime}+q(t) \max _{[\sigma(t), t]} x^\alpha(s)=0, t \geq t_0 \geq 0
$$
where $\alpha$ is a ratio of odd positive integers and $\int_{t_0}^{\infty} \frac{1}{a^{1 / \alpha}(t)} d t=\infty$. We establish a new condition which guarantees that every solution 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

Mathematics Subject Classification:

34K15

Authors Imprint References Funding Related Articles Downloads

R. Arul Department of Mathematics, Kandaswami Kandar’s College, Velur–638 182, Tamil Nadu, India.
M. Mani Department of Mathematics, Kandaswami Kandar’s College, Velur–638 182, Tamil Nadu, India.

Pages: 489-496
Date Published: 01-10-2014
Vol. 2 No. 04 (2014): Malaya Journal of Matematik (MJM)

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