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Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation

Authors:

Institution:

(1) P.G Department of Mathematics, Khallikote Autonomous College, Berhampur, 760001, Orissa, India;(2) Department of Mathematics, Berhampur University, Berhampur, 760007, Orissa, India;(3) Department of Mathematics, K.I.S.T, Bhubaneswar, Orissa, India

Abstract:

In this paper, necessary and sufficient conditions for the oscillation and asymptotic behaviour of solutions of the second order neutral delay differential equation (NDDE)

$\left {r(t)(y(t) - p(t)y(t - \tau ))'} \right]^\prime + q(t)G(y(h(t))) = 0$

are obtained, where q, h ∈ C(0, ∞), ℝ) such that q(t) ≥ 0, r ∈ C ⁽¹⁾ (0, ∞), (0, ∞)), p ∈ C (0, ∞), ℝ), G ∈ C (ℝ, ℝ) and τ ∈ ℝ⁺. Since the results of this paper hold when r(t) ≡ 1 and G(u) ≡ u, therefore it extends, generalizes and improves some known results.

Keywords:

neutral differential equation oscillation non-oscillation

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